1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2009 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_MAX_MATCHING_H |
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20 | #define LEMON_MAX_MATCHING_H |
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21 | |
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22 | #include <vector> |
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23 | #include <queue> |
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24 | #include <set> |
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25 | #include <limits> |
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26 | |
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27 | #include <lemon/core.h> |
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28 | #include <lemon/unionfind.h> |
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29 | #include <lemon/bin_heap.h> |
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30 | #include <lemon/maps.h> |
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31 | |
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32 | ///\ingroup matching |
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33 | ///\file |
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34 | ///\brief Maximum matching algorithms in general graphs. |
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35 | |
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36 | namespace lemon { |
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37 | |
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38 | /// \ingroup matching |
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39 | /// |
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40 | /// \brief Maximum cardinality matching in general graphs |
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41 | /// |
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42 | /// This class implements Edmonds' alternating forest matching algorithm |
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43 | /// for finding a maximum cardinality matching in a general undirected graph. |
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44 | /// It can be started from an arbitrary initial matching |
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45 | /// (the default is the empty one). |
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46 | /// |
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47 | /// The dual solution of the problem is a map of the nodes to |
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48 | /// \ref MaxMatching::Status "Status", having values \c EVEN (or \c D), |
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49 | /// \c ODD (or \c A) and \c MATCHED (or \c C) defining the Gallai-Edmonds |
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50 | /// decomposition of the graph. The nodes in \c EVEN/D induce a subgraph |
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51 | /// with factor-critical components, the nodes in \c ODD/A form the |
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52 | /// canonical barrier, and the nodes in \c MATCHED/C induce a graph having |
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53 | /// a perfect matching. The number of the factor-critical components |
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54 | /// minus the number of barrier nodes is a lower bound on the |
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55 | /// unmatched nodes, and the matching is optimal if and only if this bound is |
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56 | /// tight. This decomposition can be obtained using \ref status() or |
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57 | /// \ref statusMap() after running the algorithm. |
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58 | /// |
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59 | /// \tparam GR The undirected graph type the algorithm runs on. |
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60 | template <typename GR> |
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61 | class MaxMatching { |
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62 | public: |
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63 | |
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64 | /// The graph type of the algorithm |
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65 | typedef GR Graph; |
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66 | /// The type of the matching map |
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67 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
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68 | MatchingMap; |
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69 | |
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70 | ///\brief Status constants for Gallai-Edmonds decomposition. |
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71 | /// |
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72 | ///These constants are used for indicating the Gallai-Edmonds |
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73 | ///decomposition of a graph. The nodes with status \c EVEN (or \c D) |
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74 | ///induce a subgraph with factor-critical components, the nodes with |
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75 | ///status \c ODD (or \c A) form the canonical barrier, and the nodes |
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76 | ///with status \c MATCHED (or \c C) induce a subgraph having a |
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77 | ///perfect matching. |
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78 | enum Status { |
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79 | EVEN = 1, ///< = 1. (\c D is an alias for \c EVEN.) |
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80 | D = 1, |
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81 | MATCHED = 0, ///< = 0. (\c C is an alias for \c MATCHED.) |
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82 | C = 0, |
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83 | ODD = -1, ///< = -1. (\c A is an alias for \c ODD.) |
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84 | A = -1, |
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85 | UNMATCHED = -2 ///< = -2. |
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86 | }; |
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87 | |
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88 | /// The type of the status map |
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89 | typedef typename Graph::template NodeMap<Status> StatusMap; |
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90 | |
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91 | private: |
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92 | |
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93 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
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94 | |
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95 | typedef UnionFindEnum<IntNodeMap> BlossomSet; |
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96 | typedef ExtendFindEnum<IntNodeMap> TreeSet; |
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97 | typedef RangeMap<Node> NodeIntMap; |
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98 | typedef MatchingMap EarMap; |
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99 | typedef std::vector<Node> NodeQueue; |
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100 | |
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101 | const Graph& _graph; |
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102 | MatchingMap* _matching; |
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103 | StatusMap* _status; |
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104 | |
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105 | EarMap* _ear; |
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106 | |
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107 | IntNodeMap* _blossom_set_index; |
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108 | BlossomSet* _blossom_set; |
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109 | NodeIntMap* _blossom_rep; |
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110 | |
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111 | IntNodeMap* _tree_set_index; |
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112 | TreeSet* _tree_set; |
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113 | |
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114 | NodeQueue _node_queue; |
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115 | int _process, _postpone, _last; |
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116 | |
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117 | int _node_num; |
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118 | |
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119 | private: |
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120 | |
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121 | void createStructures() { |
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122 | _node_num = countNodes(_graph); |
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123 | if (!_matching) { |
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124 | _matching = new MatchingMap(_graph); |
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125 | } |
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126 | if (!_status) { |
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127 | _status = new StatusMap(_graph); |
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128 | } |
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129 | if (!_ear) { |
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130 | _ear = new EarMap(_graph); |
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131 | } |
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132 | if (!_blossom_set) { |
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133 | _blossom_set_index = new IntNodeMap(_graph); |
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134 | _blossom_set = new BlossomSet(*_blossom_set_index); |
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135 | } |
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136 | if (!_blossom_rep) { |
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137 | _blossom_rep = new NodeIntMap(_node_num); |
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138 | } |
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139 | if (!_tree_set) { |
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140 | _tree_set_index = new IntNodeMap(_graph); |
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141 | _tree_set = new TreeSet(*_tree_set_index); |
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142 | } |
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143 | _node_queue.resize(_node_num); |
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144 | } |
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145 | |
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146 | void destroyStructures() { |
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147 | if (_matching) { |
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148 | delete _matching; |
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149 | } |
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150 | if (_status) { |
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151 | delete _status; |
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152 | } |
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153 | if (_ear) { |
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154 | delete _ear; |
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155 | } |
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156 | if (_blossom_set) { |
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157 | delete _blossom_set; |
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158 | delete _blossom_set_index; |
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159 | } |
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160 | if (_blossom_rep) { |
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161 | delete _blossom_rep; |
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162 | } |
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163 | if (_tree_set) { |
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164 | delete _tree_set_index; |
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165 | delete _tree_set; |
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166 | } |
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167 | } |
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168 | |
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169 | void processDense(const Node& n) { |
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170 | _process = _postpone = _last = 0; |
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171 | _node_queue[_last++] = n; |
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172 | |
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173 | while (_process != _last) { |
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174 | Node u = _node_queue[_process++]; |
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175 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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176 | Node v = _graph.target(a); |
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177 | if ((*_status)[v] == MATCHED) { |
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178 | extendOnArc(a); |
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179 | } else if ((*_status)[v] == UNMATCHED) { |
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180 | augmentOnArc(a); |
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181 | return; |
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182 | } |
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183 | } |
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184 | } |
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185 | |
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186 | while (_postpone != _last) { |
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187 | Node u = _node_queue[_postpone++]; |
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188 | |
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189 | for (OutArcIt a(_graph, u); a != INVALID ; ++a) { |
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190 | Node v = _graph.target(a); |
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191 | |
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192 | if ((*_status)[v] == EVEN) { |
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193 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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194 | shrinkOnEdge(a); |
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195 | } |
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196 | } |
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197 | |
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198 | while (_process != _last) { |
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199 | Node w = _node_queue[_process++]; |
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200 | for (OutArcIt b(_graph, w); b != INVALID; ++b) { |
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201 | Node x = _graph.target(b); |
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202 | if ((*_status)[x] == MATCHED) { |
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203 | extendOnArc(b); |
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204 | } else if ((*_status)[x] == UNMATCHED) { |
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205 | augmentOnArc(b); |
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206 | return; |
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207 | } |
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208 | } |
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209 | } |
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210 | } |
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211 | } |
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212 | } |
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213 | |
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214 | void processSparse(const Node& n) { |
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215 | _process = _last = 0; |
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216 | _node_queue[_last++] = n; |
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217 | while (_process != _last) { |
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218 | Node u = _node_queue[_process++]; |
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219 | for (OutArcIt a(_graph, u); a != INVALID; ++a) { |
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220 | Node v = _graph.target(a); |
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221 | |
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222 | if ((*_status)[v] == EVEN) { |
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223 | if (_blossom_set->find(u) != _blossom_set->find(v)) { |
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224 | shrinkOnEdge(a); |
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225 | } |
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226 | } else if ((*_status)[v] == MATCHED) { |
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227 | extendOnArc(a); |
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228 | } else if ((*_status)[v] == UNMATCHED) { |
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229 | augmentOnArc(a); |
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230 | return; |
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231 | } |
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232 | } |
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233 | } |
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234 | } |
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235 | |
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236 | void shrinkOnEdge(const Edge& e) { |
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237 | Node nca = INVALID; |
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238 | |
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239 | { |
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240 | std::set<Node> left_set, right_set; |
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241 | |
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242 | Node left = (*_blossom_rep)[_blossom_set->find(_graph.u(e))]; |
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243 | left_set.insert(left); |
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244 | |
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245 | Node right = (*_blossom_rep)[_blossom_set->find(_graph.v(e))]; |
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246 | right_set.insert(right); |
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247 | |
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248 | while (true) { |
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249 | if ((*_matching)[left] == INVALID) break; |
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250 | left = _graph.target((*_matching)[left]); |
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251 | left = (*_blossom_rep)[_blossom_set-> |
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252 | find(_graph.target((*_ear)[left]))]; |
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253 | if (right_set.find(left) != right_set.end()) { |
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254 | nca = left; |
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255 | break; |
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256 | } |
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257 | left_set.insert(left); |
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258 | |
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259 | if ((*_matching)[right] == INVALID) break; |
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260 | right = _graph.target((*_matching)[right]); |
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261 | right = (*_blossom_rep)[_blossom_set-> |
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262 | find(_graph.target((*_ear)[right]))]; |
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263 | if (left_set.find(right) != left_set.end()) { |
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264 | nca = right; |
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265 | break; |
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266 | } |
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267 | right_set.insert(right); |
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268 | } |
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269 | |
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270 | if (nca == INVALID) { |
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271 | if ((*_matching)[left] == INVALID) { |
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272 | nca = right; |
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273 | while (left_set.find(nca) == left_set.end()) { |
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274 | nca = _graph.target((*_matching)[nca]); |
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275 | nca =(*_blossom_rep)[_blossom_set-> |
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276 | find(_graph.target((*_ear)[nca]))]; |
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277 | } |
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278 | } else { |
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279 | nca = left; |
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280 | while (right_set.find(nca) == right_set.end()) { |
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281 | nca = _graph.target((*_matching)[nca]); |
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282 | nca = (*_blossom_rep)[_blossom_set-> |
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283 | find(_graph.target((*_ear)[nca]))]; |
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284 | } |
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285 | } |
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286 | } |
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287 | } |
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288 | |
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289 | { |
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290 | |
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291 | Node node = _graph.u(e); |
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292 | Arc arc = _graph.direct(e, true); |
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293 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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294 | |
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295 | while (base != nca) { |
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296 | (*_ear)[node] = arc; |
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297 | |
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298 | Node n = node; |
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299 | while (n != base) { |
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300 | n = _graph.target((*_matching)[n]); |
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301 | Arc a = (*_ear)[n]; |
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302 | n = _graph.target(a); |
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303 | (*_ear)[n] = _graph.oppositeArc(a); |
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304 | } |
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305 | node = _graph.target((*_matching)[base]); |
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306 | _tree_set->erase(base); |
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307 | _tree_set->erase(node); |
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308 | _blossom_set->insert(node, _blossom_set->find(base)); |
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309 | (*_status)[node] = EVEN; |
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310 | _node_queue[_last++] = node; |
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311 | arc = _graph.oppositeArc((*_ear)[node]); |
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312 | node = _graph.target((*_ear)[node]); |
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313 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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314 | _blossom_set->join(_graph.target(arc), base); |
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315 | } |
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316 | } |
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317 | |
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318 | (*_blossom_rep)[_blossom_set->find(nca)] = nca; |
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319 | |
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320 | { |
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321 | |
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322 | Node node = _graph.v(e); |
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323 | Arc arc = _graph.direct(e, false); |
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324 | Node base = (*_blossom_rep)[_blossom_set->find(node)]; |
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325 | |
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326 | while (base != nca) { |
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327 | (*_ear)[node] = arc; |
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328 | |
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329 | Node n = node; |
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330 | while (n != base) { |
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331 | n = _graph.target((*_matching)[n]); |
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332 | Arc a = (*_ear)[n]; |
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333 | n = _graph.target(a); |
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334 | (*_ear)[n] = _graph.oppositeArc(a); |
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335 | } |
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336 | node = _graph.target((*_matching)[base]); |
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337 | _tree_set->erase(base); |
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338 | _tree_set->erase(node); |
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339 | _blossom_set->insert(node, _blossom_set->find(base)); |
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340 | (*_status)[node] = EVEN; |
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341 | _node_queue[_last++] = node; |
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342 | arc = _graph.oppositeArc((*_ear)[node]); |
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343 | node = _graph.target((*_ear)[node]); |
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344 | base = (*_blossom_rep)[_blossom_set->find(node)]; |
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345 | _blossom_set->join(_graph.target(arc), base); |
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346 | } |
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347 | } |
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348 | |
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349 | (*_blossom_rep)[_blossom_set->find(nca)] = nca; |
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350 | } |
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351 | |
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352 | void extendOnArc(const Arc& a) { |
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353 | Node base = _graph.source(a); |
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354 | Node odd = _graph.target(a); |
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355 | |
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356 | (*_ear)[odd] = _graph.oppositeArc(a); |
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357 | Node even = _graph.target((*_matching)[odd]); |
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358 | (*_blossom_rep)[_blossom_set->insert(even)] = even; |
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359 | (*_status)[odd] = ODD; |
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360 | (*_status)[even] = EVEN; |
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361 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(base)]); |
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362 | _tree_set->insert(odd, tree); |
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363 | _tree_set->insert(even, tree); |
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364 | _node_queue[_last++] = even; |
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365 | |
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366 | } |
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367 | |
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368 | void augmentOnArc(const Arc& a) { |
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369 | Node even = _graph.source(a); |
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370 | Node odd = _graph.target(a); |
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371 | |
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372 | int tree = _tree_set->find((*_blossom_rep)[_blossom_set->find(even)]); |
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373 | |
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374 | (*_matching)[odd] = _graph.oppositeArc(a); |
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375 | (*_status)[odd] = MATCHED; |
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376 | |
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377 | Arc arc = (*_matching)[even]; |
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378 | (*_matching)[even] = a; |
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379 | |
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380 | while (arc != INVALID) { |
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381 | odd = _graph.target(arc); |
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382 | arc = (*_ear)[odd]; |
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383 | even = _graph.target(arc); |
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384 | (*_matching)[odd] = arc; |
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385 | arc = (*_matching)[even]; |
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386 | (*_matching)[even] = _graph.oppositeArc((*_matching)[odd]); |
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387 | } |
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388 | |
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389 | for (typename TreeSet::ItemIt it(*_tree_set, tree); |
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390 | it != INVALID; ++it) { |
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391 | if ((*_status)[it] == ODD) { |
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392 | (*_status)[it] = MATCHED; |
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393 | } else { |
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394 | int blossom = _blossom_set->find(it); |
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395 | for (typename BlossomSet::ItemIt jt(*_blossom_set, blossom); |
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396 | jt != INVALID; ++jt) { |
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397 | (*_status)[jt] = MATCHED; |
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398 | } |
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399 | _blossom_set->eraseClass(blossom); |
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400 | } |
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401 | } |
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402 | _tree_set->eraseClass(tree); |
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403 | |
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404 | } |
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405 | |
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406 | public: |
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407 | |
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408 | /// \brief Constructor |
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409 | /// |
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410 | /// Constructor. |
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411 | MaxMatching(const Graph& graph) |
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412 | : _graph(graph), _matching(0), _status(0), _ear(0), |
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413 | _blossom_set_index(0), _blossom_set(0), _blossom_rep(0), |
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414 | _tree_set_index(0), _tree_set(0) {} |
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415 | |
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416 | ~MaxMatching() { |
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417 | destroyStructures(); |
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418 | } |
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419 | |
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420 | /// \name Execution Control |
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421 | /// The simplest way to execute the algorithm is to use the |
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422 | /// \c run() member function.\n |
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423 | /// If you need better control on the execution, you have to call |
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424 | /// one of the functions \ref init(), \ref greedyInit() or |
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425 | /// \ref matchingInit() first, then you can start the algorithm with |
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426 | /// \ref startSparse() or \ref startDense(). |
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427 | |
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428 | ///@{ |
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429 | |
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430 | /// \brief Set the initial matching to the empty matching. |
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431 | /// |
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432 | /// This function sets the initial matching to the empty matching. |
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433 | void init() { |
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434 | createStructures(); |
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435 | for(NodeIt n(_graph); n != INVALID; ++n) { |
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436 | (*_matching)[n] = INVALID; |
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437 | (*_status)[n] = UNMATCHED; |
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438 | } |
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439 | } |
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440 | |
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441 | /// \brief Find an initial matching in a greedy way. |
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442 | /// |
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443 | /// This function finds an initial matching in a greedy way. |
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444 | void greedyInit() { |
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445 | createStructures(); |
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446 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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447 | (*_matching)[n] = INVALID; |
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448 | (*_status)[n] = UNMATCHED; |
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449 | } |
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450 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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451 | if ((*_matching)[n] == INVALID) { |
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452 | for (OutArcIt a(_graph, n); a != INVALID ; ++a) { |
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453 | Node v = _graph.target(a); |
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454 | if ((*_matching)[v] == INVALID && v != n) { |
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455 | (*_matching)[n] = a; |
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456 | (*_status)[n] = MATCHED; |
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457 | (*_matching)[v] = _graph.oppositeArc(a); |
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458 | (*_status)[v] = MATCHED; |
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459 | break; |
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460 | } |
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461 | } |
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462 | } |
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463 | } |
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464 | } |
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465 | |
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466 | |
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467 | /// \brief Initialize the matching from a map. |
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468 | /// |
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469 | /// This function initializes the matching from a \c bool valued edge |
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470 | /// map. This map should have the property that there are no two incident |
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471 | /// edges with \c true value, i.e. it really contains a matching. |
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472 | /// \return \c true if the map contains a matching. |
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473 | template <typename MatchingMap> |
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474 | bool matchingInit(const MatchingMap& matching) { |
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475 | createStructures(); |
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476 | |
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477 | for (NodeIt n(_graph); n != INVALID; ++n) { |
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478 | (*_matching)[n] = INVALID; |
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479 | (*_status)[n] = UNMATCHED; |
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480 | } |
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481 | for(EdgeIt e(_graph); e!=INVALID; ++e) { |
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482 | if (matching[e]) { |
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483 | |
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484 | Node u = _graph.u(e); |
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485 | if ((*_matching)[u] != INVALID) return false; |
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486 | (*_matching)[u] = _graph.direct(e, true); |
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487 | (*_status)[u] = MATCHED; |
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488 | |
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489 | Node v = _graph.v(e); |
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490 | if ((*_matching)[v] != INVALID) return false; |
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491 | (*_matching)[v] = _graph.direct(e, false); |
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492 | (*_status)[v] = MATCHED; |
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493 | } |
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494 | } |
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495 | return true; |
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496 | } |
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497 | |
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498 | /// \brief Start Edmonds' algorithm |
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499 | /// |
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500 | /// This function runs the original Edmonds' algorithm. |
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501 | /// |
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502 | /// \pre \ref Init(), \ref greedyInit() or \ref matchingInit() must be |
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503 | /// called before using this function. |
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504 | void startSparse() { |
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505 | for(NodeIt n(_graph); n != INVALID; ++n) { |
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506 | if ((*_status)[n] == UNMATCHED) { |
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507 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
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508 | _tree_set->insert(n); |
---|
509 | (*_status)[n] = EVEN; |
---|
510 | processSparse(n); |
---|
511 | } |
---|
512 | } |
---|
513 | } |
---|
514 | |
---|
515 | /// \brief Start Edmonds' algorithm with a heuristic improvement |
---|
516 | /// for dense graphs |
---|
517 | /// |
---|
518 | /// This function runs Edmonds' algorithm with a heuristic of postponing |
---|
519 | /// shrinks, therefore resulting in a faster algorithm for dense graphs. |
---|
520 | /// |
---|
521 | /// \pre \ref Init(), \ref greedyInit() or \ref matchingInit() must be |
---|
522 | /// called before using this function. |
---|
523 | void startDense() { |
---|
524 | for(NodeIt n(_graph); n != INVALID; ++n) { |
---|
525 | if ((*_status)[n] == UNMATCHED) { |
---|
526 | (*_blossom_rep)[_blossom_set->insert(n)] = n; |
---|
527 | _tree_set->insert(n); |
---|
528 | (*_status)[n] = EVEN; |
---|
529 | processDense(n); |
---|
530 | } |
---|
531 | } |
---|
532 | } |
---|
533 | |
---|
534 | |
---|
535 | /// \brief Run Edmonds' algorithm |
---|
536 | /// |
---|
537 | /// This function runs Edmonds' algorithm. An additional heuristic of |
---|
538 | /// postponing shrinks is used for relatively dense graphs |
---|
539 | /// (for which <tt>m>=2*n</tt> holds). |
---|
540 | void run() { |
---|
541 | if (countEdges(_graph) < 2 * countNodes(_graph)) { |
---|
542 | greedyInit(); |
---|
543 | startSparse(); |
---|
544 | } else { |
---|
545 | init(); |
---|
546 | startDense(); |
---|
547 | } |
---|
548 | } |
---|
549 | |
---|
550 | /// @} |
---|
551 | |
---|
552 | /// \name Primal Solution |
---|
553 | /// Functions to get the primal solution, i.e. the maximum matching. |
---|
554 | |
---|
555 | /// @{ |
---|
556 | |
---|
557 | /// \brief Return the size (cardinality) of the matching. |
---|
558 | /// |
---|
559 | /// This function returns the size (cardinality) of the current matching. |
---|
560 | /// After run() it returns the size of the maximum matching in the graph. |
---|
561 | int matchingSize() const { |
---|
562 | int size = 0; |
---|
563 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
564 | if ((*_matching)[n] != INVALID) { |
---|
565 | ++size; |
---|
566 | } |
---|
567 | } |
---|
568 | return size / 2; |
---|
569 | } |
---|
570 | |
---|
571 | /// \brief Return \c true if the given edge is in the matching. |
---|
572 | /// |
---|
573 | /// This function returns \c true if the given edge is in the current |
---|
574 | /// matching. |
---|
575 | bool matching(const Edge& edge) const { |
---|
576 | return edge == (*_matching)[_graph.u(edge)]; |
---|
577 | } |
---|
578 | |
---|
579 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
580 | /// |
---|
581 | /// This function returns the matching arc (or edge) incident to the |
---|
582 | /// given node in the current matching or \c INVALID if the node is |
---|
583 | /// not covered by the matching. |
---|
584 | Arc matching(const Node& n) const { |
---|
585 | return (*_matching)[n]; |
---|
586 | } |
---|
587 | |
---|
588 | /// \brief Return a const reference to the matching map. |
---|
589 | /// |
---|
590 | /// This function returns a const reference to a node map that stores |
---|
591 | /// the matching arc (or edge) incident to each node. |
---|
592 | const MatchingMap& matchingMap() const { |
---|
593 | return *_matching; |
---|
594 | } |
---|
595 | |
---|
596 | /// \brief Return the mate of the given node. |
---|
597 | /// |
---|
598 | /// This function returns the mate of the given node in the current |
---|
599 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
600 | Node mate(const Node& n) const { |
---|
601 | return (*_matching)[n] != INVALID ? |
---|
602 | _graph.target((*_matching)[n]) : INVALID; |
---|
603 | } |
---|
604 | |
---|
605 | /// @} |
---|
606 | |
---|
607 | /// \name Dual Solution |
---|
608 | /// Functions to get the dual solution, i.e. the Gallai-Edmonds |
---|
609 | /// decomposition. |
---|
610 | |
---|
611 | /// @{ |
---|
612 | |
---|
613 | /// \brief Return the status of the given node in the Edmonds-Gallai |
---|
614 | /// decomposition. |
---|
615 | /// |
---|
616 | /// This function returns the \ref Status "status" of the given node |
---|
617 | /// in the Edmonds-Gallai decomposition. |
---|
618 | Status status(const Node& n) const { |
---|
619 | return (*_status)[n]; |
---|
620 | } |
---|
621 | |
---|
622 | /// \brief Return a const reference to the status map, which stores |
---|
623 | /// the Edmonds-Gallai decomposition. |
---|
624 | /// |
---|
625 | /// This function returns a const reference to a node map that stores the |
---|
626 | /// \ref Status "status" of each node in the Edmonds-Gallai decomposition. |
---|
627 | const StatusMap& statusMap() const { |
---|
628 | return *_status; |
---|
629 | } |
---|
630 | |
---|
631 | /// \brief Return \c true if the given node is in the barrier. |
---|
632 | /// |
---|
633 | /// This function returns \c true if the given node is in the barrier. |
---|
634 | bool barrier(const Node& n) const { |
---|
635 | return (*_status)[n] == ODD; |
---|
636 | } |
---|
637 | |
---|
638 | /// @} |
---|
639 | |
---|
640 | }; |
---|
641 | |
---|
642 | /// \ingroup matching |
---|
643 | /// |
---|
644 | /// \brief Weighted matching in general graphs |
---|
645 | /// |
---|
646 | /// This class provides an efficient implementation of Edmond's |
---|
647 | /// maximum weighted matching algorithm. The implementation is based |
---|
648 | /// on extensive use of priority queues and provides |
---|
649 | /// \f$O(nm\log n)\f$ time complexity. |
---|
650 | /// |
---|
651 | /// The maximum weighted matching problem is to find a subset of the |
---|
652 | /// edges in an undirected graph with maximum overall weight for which |
---|
653 | /// each node has at most one incident edge. |
---|
654 | /// It can be formulated with the following linear program. |
---|
655 | /// \f[ \sum_{e \in \delta(u)}x_e \le 1 \quad \forall u\in V\f] |
---|
656 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
657 | \quad \forall B\in\mathcal{O}\f] */ |
---|
658 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
659 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
660 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
661 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
662 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
663 | /// subsets of the nodes. |
---|
664 | /// |
---|
665 | /// The algorithm calculates an optimal matching and a proof of the |
---|
666 | /// optimality. The solution of the dual problem can be used to check |
---|
667 | /// the result of the algorithm. The dual linear problem is the |
---|
668 | /// following. |
---|
669 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)} |
---|
670 | z_B \ge w_{uv} \quad \forall uv\in E\f] */ |
---|
671 | /// \f[y_u \ge 0 \quad \forall u \in V\f] |
---|
672 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
673 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
674 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
675 | /// |
---|
676 | /// The algorithm can be executed with the run() function. |
---|
677 | /// After it the matching (the primal solution) and the dual solution |
---|
678 | /// can be obtained using the query functions and the |
---|
679 | /// \ref MaxWeightedMatching::BlossomIt "BlossomIt" nested class, |
---|
680 | /// which is able to iterate on the nodes of a blossom. |
---|
681 | /// If the value type is integer, then the dual solution is multiplied |
---|
682 | /// by \ref MaxWeightedMatching::dualScale "4". |
---|
683 | /// |
---|
684 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
685 | /// \tparam WM The type edge weight map. The default type is |
---|
686 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
687 | #ifdef DOXYGEN |
---|
688 | template <typename GR, typename WM> |
---|
689 | #else |
---|
690 | template <typename GR, |
---|
691 | typename WM = typename GR::template EdgeMap<int> > |
---|
692 | #endif |
---|
693 | class MaxWeightedMatching { |
---|
694 | public: |
---|
695 | |
---|
696 | /// The graph type of the algorithm |
---|
697 | typedef GR Graph; |
---|
698 | /// The type of the edge weight map |
---|
699 | typedef WM WeightMap; |
---|
700 | /// The value type of the edge weights |
---|
701 | typedef typename WeightMap::Value Value; |
---|
702 | |
---|
703 | /// The type of the matching map |
---|
704 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
705 | MatchingMap; |
---|
706 | |
---|
707 | /// \brief Scaling factor for dual solution |
---|
708 | /// |
---|
709 | /// Scaling factor for dual solution. It is equal to 4 or 1 |
---|
710 | /// according to the value type. |
---|
711 | static const int dualScale = |
---|
712 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
713 | |
---|
714 | private: |
---|
715 | |
---|
716 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
717 | |
---|
718 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
719 | typedef std::vector<Node> BlossomNodeList; |
---|
720 | |
---|
721 | struct BlossomVariable { |
---|
722 | int begin, end; |
---|
723 | Value value; |
---|
724 | |
---|
725 | BlossomVariable(int _begin, int _end, Value _value) |
---|
726 | : begin(_begin), end(_end), value(_value) {} |
---|
727 | |
---|
728 | }; |
---|
729 | |
---|
730 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
731 | |
---|
732 | const Graph& _graph; |
---|
733 | const WeightMap& _weight; |
---|
734 | |
---|
735 | MatchingMap* _matching; |
---|
736 | |
---|
737 | NodePotential* _node_potential; |
---|
738 | |
---|
739 | BlossomPotential _blossom_potential; |
---|
740 | BlossomNodeList _blossom_node_list; |
---|
741 | |
---|
742 | int _node_num; |
---|
743 | int _blossom_num; |
---|
744 | |
---|
745 | typedef RangeMap<int> IntIntMap; |
---|
746 | |
---|
747 | enum Status { |
---|
748 | EVEN = -1, MATCHED = 0, ODD = 1, UNMATCHED = -2 |
---|
749 | }; |
---|
750 | |
---|
751 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
752 | struct BlossomData { |
---|
753 | int tree; |
---|
754 | Status status; |
---|
755 | Arc pred, next; |
---|
756 | Value pot, offset; |
---|
757 | Node base; |
---|
758 | }; |
---|
759 | |
---|
760 | IntNodeMap *_blossom_index; |
---|
761 | BlossomSet *_blossom_set; |
---|
762 | RangeMap<BlossomData>* _blossom_data; |
---|
763 | |
---|
764 | IntNodeMap *_node_index; |
---|
765 | IntArcMap *_node_heap_index; |
---|
766 | |
---|
767 | struct NodeData { |
---|
768 | |
---|
769 | NodeData(IntArcMap& node_heap_index) |
---|
770 | : heap(node_heap_index) {} |
---|
771 | |
---|
772 | int blossom; |
---|
773 | Value pot; |
---|
774 | BinHeap<Value, IntArcMap> heap; |
---|
775 | std::map<int, Arc> heap_index; |
---|
776 | |
---|
777 | int tree; |
---|
778 | }; |
---|
779 | |
---|
780 | RangeMap<NodeData>* _node_data; |
---|
781 | |
---|
782 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
783 | |
---|
784 | IntIntMap *_tree_set_index; |
---|
785 | TreeSet *_tree_set; |
---|
786 | |
---|
787 | IntNodeMap *_delta1_index; |
---|
788 | BinHeap<Value, IntNodeMap> *_delta1; |
---|
789 | |
---|
790 | IntIntMap *_delta2_index; |
---|
791 | BinHeap<Value, IntIntMap> *_delta2; |
---|
792 | |
---|
793 | IntEdgeMap *_delta3_index; |
---|
794 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
795 | |
---|
796 | IntIntMap *_delta4_index; |
---|
797 | BinHeap<Value, IntIntMap> *_delta4; |
---|
798 | |
---|
799 | Value _delta_sum; |
---|
800 | |
---|
801 | void createStructures() { |
---|
802 | _node_num = countNodes(_graph); |
---|
803 | _blossom_num = _node_num * 3 / 2; |
---|
804 | |
---|
805 | if (!_matching) { |
---|
806 | _matching = new MatchingMap(_graph); |
---|
807 | } |
---|
808 | if (!_node_potential) { |
---|
809 | _node_potential = new NodePotential(_graph); |
---|
810 | } |
---|
811 | if (!_blossom_set) { |
---|
812 | _blossom_index = new IntNodeMap(_graph); |
---|
813 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
814 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
815 | } |
---|
816 | |
---|
817 | if (!_node_index) { |
---|
818 | _node_index = new IntNodeMap(_graph); |
---|
819 | _node_heap_index = new IntArcMap(_graph); |
---|
820 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
821 | NodeData(*_node_heap_index)); |
---|
822 | } |
---|
823 | |
---|
824 | if (!_tree_set) { |
---|
825 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
826 | _tree_set = new TreeSet(*_tree_set_index); |
---|
827 | } |
---|
828 | if (!_delta1) { |
---|
829 | _delta1_index = new IntNodeMap(_graph); |
---|
830 | _delta1 = new BinHeap<Value, IntNodeMap>(*_delta1_index); |
---|
831 | } |
---|
832 | if (!_delta2) { |
---|
833 | _delta2_index = new IntIntMap(_blossom_num); |
---|
834 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
835 | } |
---|
836 | if (!_delta3) { |
---|
837 | _delta3_index = new IntEdgeMap(_graph); |
---|
838 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
839 | } |
---|
840 | if (!_delta4) { |
---|
841 | _delta4_index = new IntIntMap(_blossom_num); |
---|
842 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
843 | } |
---|
844 | } |
---|
845 | |
---|
846 | void destroyStructures() { |
---|
847 | _node_num = countNodes(_graph); |
---|
848 | _blossom_num = _node_num * 3 / 2; |
---|
849 | |
---|
850 | if (_matching) { |
---|
851 | delete _matching; |
---|
852 | } |
---|
853 | if (_node_potential) { |
---|
854 | delete _node_potential; |
---|
855 | } |
---|
856 | if (_blossom_set) { |
---|
857 | delete _blossom_index; |
---|
858 | delete _blossom_set; |
---|
859 | delete _blossom_data; |
---|
860 | } |
---|
861 | |
---|
862 | if (_node_index) { |
---|
863 | delete _node_index; |
---|
864 | delete _node_heap_index; |
---|
865 | delete _node_data; |
---|
866 | } |
---|
867 | |
---|
868 | if (_tree_set) { |
---|
869 | delete _tree_set_index; |
---|
870 | delete _tree_set; |
---|
871 | } |
---|
872 | if (_delta1) { |
---|
873 | delete _delta1_index; |
---|
874 | delete _delta1; |
---|
875 | } |
---|
876 | if (_delta2) { |
---|
877 | delete _delta2_index; |
---|
878 | delete _delta2; |
---|
879 | } |
---|
880 | if (_delta3) { |
---|
881 | delete _delta3_index; |
---|
882 | delete _delta3; |
---|
883 | } |
---|
884 | if (_delta4) { |
---|
885 | delete _delta4_index; |
---|
886 | delete _delta4; |
---|
887 | } |
---|
888 | } |
---|
889 | |
---|
890 | void matchedToEven(int blossom, int tree) { |
---|
891 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
892 | _delta2->erase(blossom); |
---|
893 | } |
---|
894 | |
---|
895 | if (!_blossom_set->trivial(blossom)) { |
---|
896 | (*_blossom_data)[blossom].pot -= |
---|
897 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
898 | } |
---|
899 | |
---|
900 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
901 | n != INVALID; ++n) { |
---|
902 | |
---|
903 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
904 | int ni = (*_node_index)[n]; |
---|
905 | |
---|
906 | (*_node_data)[ni].heap.clear(); |
---|
907 | (*_node_data)[ni].heap_index.clear(); |
---|
908 | |
---|
909 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
910 | |
---|
911 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
912 | |
---|
913 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
914 | Node v = _graph.source(e); |
---|
915 | int vb = _blossom_set->find(v); |
---|
916 | int vi = (*_node_index)[v]; |
---|
917 | |
---|
918 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
919 | dualScale * _weight[e]; |
---|
920 | |
---|
921 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
922 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
923 | _delta3->push(e, rw / 2); |
---|
924 | } |
---|
925 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
926 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
927 | _delta3->push(e, rw); |
---|
928 | } |
---|
929 | } else { |
---|
930 | typename std::map<int, Arc>::iterator it = |
---|
931 | (*_node_data)[vi].heap_index.find(tree); |
---|
932 | |
---|
933 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
934 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
935 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
936 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
937 | it->second = e; |
---|
938 | } |
---|
939 | } else { |
---|
940 | (*_node_data)[vi].heap.push(e, rw); |
---|
941 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
942 | } |
---|
943 | |
---|
944 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
945 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
946 | |
---|
947 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
948 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
949 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
950 | (*_blossom_data)[vb].offset); |
---|
951 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
952 | (*_blossom_data)[vb].offset){ |
---|
953 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
954 | (*_blossom_data)[vb].offset); |
---|
955 | } |
---|
956 | } |
---|
957 | } |
---|
958 | } |
---|
959 | } |
---|
960 | } |
---|
961 | (*_blossom_data)[blossom].offset = 0; |
---|
962 | } |
---|
963 | |
---|
964 | void matchedToOdd(int blossom) { |
---|
965 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
966 | _delta2->erase(blossom); |
---|
967 | } |
---|
968 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
969 | if (!_blossom_set->trivial(blossom)) { |
---|
970 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
971 | (*_blossom_data)[blossom].offset); |
---|
972 | } |
---|
973 | } |
---|
974 | |
---|
975 | void evenToMatched(int blossom, int tree) { |
---|
976 | if (!_blossom_set->trivial(blossom)) { |
---|
977 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
978 | } |
---|
979 | |
---|
980 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
981 | n != INVALID; ++n) { |
---|
982 | int ni = (*_node_index)[n]; |
---|
983 | (*_node_data)[ni].pot -= _delta_sum; |
---|
984 | |
---|
985 | _delta1->erase(n); |
---|
986 | |
---|
987 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
988 | Node v = _graph.source(e); |
---|
989 | int vb = _blossom_set->find(v); |
---|
990 | int vi = (*_node_index)[v]; |
---|
991 | |
---|
992 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
993 | dualScale * _weight[e]; |
---|
994 | |
---|
995 | if (vb == blossom) { |
---|
996 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
997 | _delta3->erase(e); |
---|
998 | } |
---|
999 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
1000 | |
---|
1001 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1002 | _delta3->erase(e); |
---|
1003 | } |
---|
1004 | |
---|
1005 | int vt = _tree_set->find(vb); |
---|
1006 | |
---|
1007 | if (vt != tree) { |
---|
1008 | |
---|
1009 | Arc r = _graph.oppositeArc(e); |
---|
1010 | |
---|
1011 | typename std::map<int, Arc>::iterator it = |
---|
1012 | (*_node_data)[ni].heap_index.find(vt); |
---|
1013 | |
---|
1014 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
1015 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
1016 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
1017 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
1018 | it->second = r; |
---|
1019 | } |
---|
1020 | } else { |
---|
1021 | (*_node_data)[ni].heap.push(r, rw); |
---|
1022 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
1023 | } |
---|
1024 | |
---|
1025 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
1026 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
1027 | |
---|
1028 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
1029 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
1030 | (*_blossom_data)[blossom].offset); |
---|
1031 | } else if ((*_delta2)[blossom] > |
---|
1032 | _blossom_set->classPrio(blossom) - |
---|
1033 | (*_blossom_data)[blossom].offset){ |
---|
1034 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
1035 | (*_blossom_data)[blossom].offset); |
---|
1036 | } |
---|
1037 | } |
---|
1038 | } |
---|
1039 | |
---|
1040 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
1041 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1042 | _delta3->erase(e); |
---|
1043 | } |
---|
1044 | } else { |
---|
1045 | |
---|
1046 | typename std::map<int, Arc>::iterator it = |
---|
1047 | (*_node_data)[vi].heap_index.find(tree); |
---|
1048 | |
---|
1049 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
1050 | (*_node_data)[vi].heap.erase(it->second); |
---|
1051 | (*_node_data)[vi].heap_index.erase(it); |
---|
1052 | if ((*_node_data)[vi].heap.empty()) { |
---|
1053 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
1054 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
1055 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
1056 | } |
---|
1057 | |
---|
1058 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
1059 | if (_blossom_set->classPrio(vb) == |
---|
1060 | std::numeric_limits<Value>::max()) { |
---|
1061 | _delta2->erase(vb); |
---|
1062 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
1063 | (*_blossom_data)[vb].offset) { |
---|
1064 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
1065 | (*_blossom_data)[vb].offset); |
---|
1066 | } |
---|
1067 | } |
---|
1068 | } |
---|
1069 | } |
---|
1070 | } |
---|
1071 | } |
---|
1072 | } |
---|
1073 | |
---|
1074 | void oddToMatched(int blossom) { |
---|
1075 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
1076 | |
---|
1077 | if (_blossom_set->classPrio(blossom) != |
---|
1078 | std::numeric_limits<Value>::max()) { |
---|
1079 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
1080 | (*_blossom_data)[blossom].offset); |
---|
1081 | } |
---|
1082 | |
---|
1083 | if (!_blossom_set->trivial(blossom)) { |
---|
1084 | _delta4->erase(blossom); |
---|
1085 | } |
---|
1086 | } |
---|
1087 | |
---|
1088 | void oddToEven(int blossom, int tree) { |
---|
1089 | if (!_blossom_set->trivial(blossom)) { |
---|
1090 | _delta4->erase(blossom); |
---|
1091 | (*_blossom_data)[blossom].pot -= |
---|
1092 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
1093 | } |
---|
1094 | |
---|
1095 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
1096 | n != INVALID; ++n) { |
---|
1097 | int ni = (*_node_index)[n]; |
---|
1098 | |
---|
1099 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
1100 | |
---|
1101 | (*_node_data)[ni].heap.clear(); |
---|
1102 | (*_node_data)[ni].heap_index.clear(); |
---|
1103 | (*_node_data)[ni].pot += |
---|
1104 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
1105 | |
---|
1106 | _delta1->push(n, (*_node_data)[ni].pot); |
---|
1107 | |
---|
1108 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
1109 | Node v = _graph.source(e); |
---|
1110 | int vb = _blossom_set->find(v); |
---|
1111 | int vi = (*_node_index)[v]; |
---|
1112 | |
---|
1113 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
1114 | dualScale * _weight[e]; |
---|
1115 | |
---|
1116 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
1117 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
1118 | _delta3->push(e, rw / 2); |
---|
1119 | } |
---|
1120 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
1121 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
1122 | _delta3->push(e, rw); |
---|
1123 | } |
---|
1124 | } else { |
---|
1125 | |
---|
1126 | typename std::map<int, Arc>::iterator it = |
---|
1127 | (*_node_data)[vi].heap_index.find(tree); |
---|
1128 | |
---|
1129 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
1130 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
1131 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
1132 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
1133 | it->second = e; |
---|
1134 | } |
---|
1135 | } else { |
---|
1136 | (*_node_data)[vi].heap.push(e, rw); |
---|
1137 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
1138 | } |
---|
1139 | |
---|
1140 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
1141 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
1142 | |
---|
1143 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
1144 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
1145 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
1146 | (*_blossom_data)[vb].offset); |
---|
1147 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
1148 | (*_blossom_data)[vb].offset) { |
---|
1149 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
1150 | (*_blossom_data)[vb].offset); |
---|
1151 | } |
---|
1152 | } |
---|
1153 | } |
---|
1154 | } |
---|
1155 | } |
---|
1156 | } |
---|
1157 | (*_blossom_data)[blossom].offset = 0; |
---|
1158 | } |
---|
1159 | |
---|
1160 | |
---|
1161 | void matchedToUnmatched(int blossom) { |
---|
1162 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
1163 | _delta2->erase(blossom); |
---|
1164 | } |
---|
1165 | |
---|
1166 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
1167 | n != INVALID; ++n) { |
---|
1168 | int ni = (*_node_index)[n]; |
---|
1169 | |
---|
1170 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
1171 | |
---|
1172 | (*_node_data)[ni].heap.clear(); |
---|
1173 | (*_node_data)[ni].heap_index.clear(); |
---|
1174 | |
---|
1175 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
1176 | Node v = _graph.target(e); |
---|
1177 | int vb = _blossom_set->find(v); |
---|
1178 | int vi = (*_node_index)[v]; |
---|
1179 | |
---|
1180 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
1181 | dualScale * _weight[e]; |
---|
1182 | |
---|
1183 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
1184 | if (_delta3->state(e) != _delta3->IN_HEAP) { |
---|
1185 | _delta3->push(e, rw); |
---|
1186 | } |
---|
1187 | } |
---|
1188 | } |
---|
1189 | } |
---|
1190 | } |
---|
1191 | |
---|
1192 | void unmatchedToMatched(int blossom) { |
---|
1193 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
1194 | n != INVALID; ++n) { |
---|
1195 | int ni = (*_node_index)[n]; |
---|
1196 | |
---|
1197 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
1198 | Node v = _graph.source(e); |
---|
1199 | int vb = _blossom_set->find(v); |
---|
1200 | int vi = (*_node_index)[v]; |
---|
1201 | |
---|
1202 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
1203 | dualScale * _weight[e]; |
---|
1204 | |
---|
1205 | if (vb == blossom) { |
---|
1206 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1207 | _delta3->erase(e); |
---|
1208 | } |
---|
1209 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
1210 | |
---|
1211 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1212 | _delta3->erase(e); |
---|
1213 | } |
---|
1214 | |
---|
1215 | int vt = _tree_set->find(vb); |
---|
1216 | |
---|
1217 | Arc r = _graph.oppositeArc(e); |
---|
1218 | |
---|
1219 | typename std::map<int, Arc>::iterator it = |
---|
1220 | (*_node_data)[ni].heap_index.find(vt); |
---|
1221 | |
---|
1222 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
1223 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
1224 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
1225 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
1226 | it->second = r; |
---|
1227 | } |
---|
1228 | } else { |
---|
1229 | (*_node_data)[ni].heap.push(r, rw); |
---|
1230 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
1231 | } |
---|
1232 | |
---|
1233 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
1234 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
1235 | |
---|
1236 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
1237 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
1238 | (*_blossom_data)[blossom].offset); |
---|
1239 | } else if ((*_delta2)[blossom] > _blossom_set->classPrio(blossom)- |
---|
1240 | (*_blossom_data)[blossom].offset){ |
---|
1241 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
1242 | (*_blossom_data)[blossom].offset); |
---|
1243 | } |
---|
1244 | } |
---|
1245 | |
---|
1246 | } else if ((*_blossom_data)[vb].status == UNMATCHED) { |
---|
1247 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
1248 | _delta3->erase(e); |
---|
1249 | } |
---|
1250 | } |
---|
1251 | } |
---|
1252 | } |
---|
1253 | } |
---|
1254 | |
---|
1255 | void alternatePath(int even, int tree) { |
---|
1256 | int odd; |
---|
1257 | |
---|
1258 | evenToMatched(even, tree); |
---|
1259 | (*_blossom_data)[even].status = MATCHED; |
---|
1260 | |
---|
1261 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
1262 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
1263 | (*_blossom_data)[odd].status = MATCHED; |
---|
1264 | oddToMatched(odd); |
---|
1265 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
1266 | |
---|
1267 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
1268 | (*_blossom_data)[even].status = MATCHED; |
---|
1269 | evenToMatched(even, tree); |
---|
1270 | (*_blossom_data)[even].next = |
---|
1271 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
1272 | } |
---|
1273 | |
---|
1274 | } |
---|
1275 | |
---|
1276 | void destroyTree(int tree) { |
---|
1277 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
1278 | if ((*_blossom_data)[b].status == EVEN) { |
---|
1279 | (*_blossom_data)[b].status = MATCHED; |
---|
1280 | evenToMatched(b, tree); |
---|
1281 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
1282 | (*_blossom_data)[b].status = MATCHED; |
---|
1283 | oddToMatched(b); |
---|
1284 | } |
---|
1285 | } |
---|
1286 | _tree_set->eraseClass(tree); |
---|
1287 | } |
---|
1288 | |
---|
1289 | |
---|
1290 | void unmatchNode(const Node& node) { |
---|
1291 | int blossom = _blossom_set->find(node); |
---|
1292 | int tree = _tree_set->find(blossom); |
---|
1293 | |
---|
1294 | alternatePath(blossom, tree); |
---|
1295 | destroyTree(tree); |
---|
1296 | |
---|
1297 | (*_blossom_data)[blossom].status = UNMATCHED; |
---|
1298 | (*_blossom_data)[blossom].base = node; |
---|
1299 | matchedToUnmatched(blossom); |
---|
1300 | } |
---|
1301 | |
---|
1302 | |
---|
1303 | void augmentOnEdge(const Edge& edge) { |
---|
1304 | |
---|
1305 | int left = _blossom_set->find(_graph.u(edge)); |
---|
1306 | int right = _blossom_set->find(_graph.v(edge)); |
---|
1307 | |
---|
1308 | if ((*_blossom_data)[left].status == EVEN) { |
---|
1309 | int left_tree = _tree_set->find(left); |
---|
1310 | alternatePath(left, left_tree); |
---|
1311 | destroyTree(left_tree); |
---|
1312 | } else { |
---|
1313 | (*_blossom_data)[left].status = MATCHED; |
---|
1314 | unmatchedToMatched(left); |
---|
1315 | } |
---|
1316 | |
---|
1317 | if ((*_blossom_data)[right].status == EVEN) { |
---|
1318 | int right_tree = _tree_set->find(right); |
---|
1319 | alternatePath(right, right_tree); |
---|
1320 | destroyTree(right_tree); |
---|
1321 | } else { |
---|
1322 | (*_blossom_data)[right].status = MATCHED; |
---|
1323 | unmatchedToMatched(right); |
---|
1324 | } |
---|
1325 | |
---|
1326 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
1327 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
1328 | } |
---|
1329 | |
---|
1330 | void extendOnArc(const Arc& arc) { |
---|
1331 | int base = _blossom_set->find(_graph.target(arc)); |
---|
1332 | int tree = _tree_set->find(base); |
---|
1333 | |
---|
1334 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
1335 | _tree_set->insert(odd, tree); |
---|
1336 | (*_blossom_data)[odd].status = ODD; |
---|
1337 | matchedToOdd(odd); |
---|
1338 | (*_blossom_data)[odd].pred = arc; |
---|
1339 | |
---|
1340 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
1341 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
1342 | _tree_set->insert(even, tree); |
---|
1343 | (*_blossom_data)[even].status = EVEN; |
---|
1344 | matchedToEven(even, tree); |
---|
1345 | } |
---|
1346 | |
---|
1347 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
1348 | int nca = -1; |
---|
1349 | std::vector<int> left_path, right_path; |
---|
1350 | |
---|
1351 | { |
---|
1352 | std::set<int> left_set, right_set; |
---|
1353 | int left = _blossom_set->find(_graph.u(edge)); |
---|
1354 | left_path.push_back(left); |
---|
1355 | left_set.insert(left); |
---|
1356 | |
---|
1357 | int right = _blossom_set->find(_graph.v(edge)); |
---|
1358 | right_path.push_back(right); |
---|
1359 | right_set.insert(right); |
---|
1360 | |
---|
1361 | while (true) { |
---|
1362 | |
---|
1363 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
1364 | |
---|
1365 | left = |
---|
1366 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
1367 | left_path.push_back(left); |
---|
1368 | left = |
---|
1369 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
1370 | left_path.push_back(left); |
---|
1371 | |
---|
1372 | left_set.insert(left); |
---|
1373 | |
---|
1374 | if (right_set.find(left) != right_set.end()) { |
---|
1375 | nca = left; |
---|
1376 | break; |
---|
1377 | } |
---|
1378 | |
---|
1379 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
1380 | |
---|
1381 | right = |
---|
1382 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
1383 | right_path.push_back(right); |
---|
1384 | right = |
---|
1385 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
1386 | right_path.push_back(right); |
---|
1387 | |
---|
1388 | right_set.insert(right); |
---|
1389 | |
---|
1390 | if (left_set.find(right) != left_set.end()) { |
---|
1391 | nca = right; |
---|
1392 | break; |
---|
1393 | } |
---|
1394 | |
---|
1395 | } |
---|
1396 | |
---|
1397 | if (nca == -1) { |
---|
1398 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
1399 | nca = right; |
---|
1400 | while (left_set.find(nca) == left_set.end()) { |
---|
1401 | nca = |
---|
1402 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
1403 | right_path.push_back(nca); |
---|
1404 | nca = |
---|
1405 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
1406 | right_path.push_back(nca); |
---|
1407 | } |
---|
1408 | } else { |
---|
1409 | nca = left; |
---|
1410 | while (right_set.find(nca) == right_set.end()) { |
---|
1411 | nca = |
---|
1412 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
1413 | left_path.push_back(nca); |
---|
1414 | nca = |
---|
1415 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
1416 | left_path.push_back(nca); |
---|
1417 | } |
---|
1418 | } |
---|
1419 | } |
---|
1420 | } |
---|
1421 | |
---|
1422 | std::vector<int> subblossoms; |
---|
1423 | Arc prev; |
---|
1424 | |
---|
1425 | prev = _graph.direct(edge, true); |
---|
1426 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
1427 | subblossoms.push_back(left_path[i]); |
---|
1428 | (*_blossom_data)[left_path[i]].next = prev; |
---|
1429 | _tree_set->erase(left_path[i]); |
---|
1430 | |
---|
1431 | subblossoms.push_back(left_path[i + 1]); |
---|
1432 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
1433 | oddToEven(left_path[i + 1], tree); |
---|
1434 | _tree_set->erase(left_path[i + 1]); |
---|
1435 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
1436 | } |
---|
1437 | |
---|
1438 | int k = 0; |
---|
1439 | while (right_path[k] != nca) ++k; |
---|
1440 | |
---|
1441 | subblossoms.push_back(nca); |
---|
1442 | (*_blossom_data)[nca].next = prev; |
---|
1443 | |
---|
1444 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
1445 | subblossoms.push_back(right_path[i + 1]); |
---|
1446 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
1447 | oddToEven(right_path[i + 1], tree); |
---|
1448 | _tree_set->erase(right_path[i + 1]); |
---|
1449 | |
---|
1450 | (*_blossom_data)[right_path[i + 1]].next = |
---|
1451 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
1452 | |
---|
1453 | subblossoms.push_back(right_path[i]); |
---|
1454 | _tree_set->erase(right_path[i]); |
---|
1455 | } |
---|
1456 | |
---|
1457 | int surface = |
---|
1458 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
1459 | |
---|
1460 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
1461 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
1462 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
1463 | } |
---|
1464 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
1465 | } |
---|
1466 | |
---|
1467 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
1468 | (*_blossom_data)[surface].offset = 0; |
---|
1469 | (*_blossom_data)[surface].status = EVEN; |
---|
1470 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
1471 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
1472 | |
---|
1473 | _tree_set->insert(surface, tree); |
---|
1474 | _tree_set->erase(nca); |
---|
1475 | } |
---|
1476 | |
---|
1477 | void splitBlossom(int blossom) { |
---|
1478 | Arc next = (*_blossom_data)[blossom].next; |
---|
1479 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
1480 | |
---|
1481 | int tree = _tree_set->find(blossom); |
---|
1482 | |
---|
1483 | (*_blossom_data)[blossom].status = MATCHED; |
---|
1484 | oddToMatched(blossom); |
---|
1485 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
1486 | _delta2->erase(blossom); |
---|
1487 | } |
---|
1488 | |
---|
1489 | std::vector<int> subblossoms; |
---|
1490 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
1491 | |
---|
1492 | Value offset = (*_blossom_data)[blossom].offset; |
---|
1493 | int b = _blossom_set->find(_graph.source(pred)); |
---|
1494 | int d = _blossom_set->find(_graph.source(next)); |
---|
1495 | |
---|
1496 | int ib = -1, id = -1; |
---|
1497 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
1498 | if (subblossoms[i] == b) ib = i; |
---|
1499 | if (subblossoms[i] == d) id = i; |
---|
1500 | |
---|
1501 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
1502 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
1503 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
1504 | } |
---|
1505 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
1506 | std::numeric_limits<Value>::max()) { |
---|
1507 | _delta2->push(subblossoms[i], |
---|
1508 | _blossom_set->classPrio(subblossoms[i]) - |
---|
1509 | (*_blossom_data)[subblossoms[i]].offset); |
---|
1510 | } |
---|
1511 | } |
---|
1512 | |
---|
1513 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
1514 | for (int i = (id + 1) % subblossoms.size(); |
---|
1515 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
1516 | int sb = subblossoms[i]; |
---|
1517 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
1518 | (*_blossom_data)[sb].next = |
---|
1519 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
1520 | } |
---|
1521 | |
---|
1522 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
1523 | int sb = subblossoms[i]; |
---|
1524 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
1525 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
1526 | |
---|
1527 | (*_blossom_data)[sb].status = ODD; |
---|
1528 | matchedToOdd(sb); |
---|
1529 | _tree_set->insert(sb, tree); |
---|
1530 | (*_blossom_data)[sb].pred = pred; |
---|
1531 | (*_blossom_data)[sb].next = |
---|
1532 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
1533 | |
---|
1534 | pred = (*_blossom_data)[ub].next; |
---|
1535 | |
---|
1536 | (*_blossom_data)[tb].status = EVEN; |
---|
1537 | matchedToEven(tb, tree); |
---|
1538 | _tree_set->insert(tb, tree); |
---|
1539 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
1540 | } |
---|
1541 | |
---|
1542 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
1543 | matchedToOdd(subblossoms[id]); |
---|
1544 | _tree_set->insert(subblossoms[id], tree); |
---|
1545 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
1546 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
1547 | |
---|
1548 | } else { |
---|
1549 | |
---|
1550 | for (int i = (ib + 1) % subblossoms.size(); |
---|
1551 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
1552 | int sb = subblossoms[i]; |
---|
1553 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
1554 | (*_blossom_data)[sb].next = |
---|
1555 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
1556 | } |
---|
1557 | |
---|
1558 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
1559 | int sb = subblossoms[i]; |
---|
1560 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
1561 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
1562 | |
---|
1563 | (*_blossom_data)[sb].status = ODD; |
---|
1564 | matchedToOdd(sb); |
---|
1565 | _tree_set->insert(sb, tree); |
---|
1566 | (*_blossom_data)[sb].next = next; |
---|
1567 | (*_blossom_data)[sb].pred = |
---|
1568 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
1569 | |
---|
1570 | (*_blossom_data)[tb].status = EVEN; |
---|
1571 | matchedToEven(tb, tree); |
---|
1572 | _tree_set->insert(tb, tree); |
---|
1573 | (*_blossom_data)[tb].pred = |
---|
1574 | (*_blossom_data)[tb].next = |
---|
1575 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
1576 | next = (*_blossom_data)[ub].next; |
---|
1577 | } |
---|
1578 | |
---|
1579 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
1580 | matchedToOdd(subblossoms[ib]); |
---|
1581 | _tree_set->insert(subblossoms[ib], tree); |
---|
1582 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
1583 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
1584 | } |
---|
1585 | _tree_set->erase(blossom); |
---|
1586 | } |
---|
1587 | |
---|
1588 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
1589 | if (_blossom_set->trivial(blossom)) { |
---|
1590 | int bi = (*_node_index)[base]; |
---|
1591 | Value pot = (*_node_data)[bi].pot; |
---|
1592 | |
---|
1593 | (*_matching)[base] = matching; |
---|
1594 | _blossom_node_list.push_back(base); |
---|
1595 | (*_node_potential)[base] = pot; |
---|
1596 | } else { |
---|
1597 | |
---|
1598 | Value pot = (*_blossom_data)[blossom].pot; |
---|
1599 | int bn = _blossom_node_list.size(); |
---|
1600 | |
---|
1601 | std::vector<int> subblossoms; |
---|
1602 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
1603 | int b = _blossom_set->find(base); |
---|
1604 | int ib = -1; |
---|
1605 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
1606 | if (subblossoms[i] == b) { ib = i; break; } |
---|
1607 | } |
---|
1608 | |
---|
1609 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
1610 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
1611 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
1612 | |
---|
1613 | Arc m = (*_blossom_data)[tb].next; |
---|
1614 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
1615 | extractBlossom(tb, _graph.source(m), m); |
---|
1616 | } |
---|
1617 | extractBlossom(subblossoms[ib], base, matching); |
---|
1618 | |
---|
1619 | int en = _blossom_node_list.size(); |
---|
1620 | |
---|
1621 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
1622 | } |
---|
1623 | } |
---|
1624 | |
---|
1625 | void extractMatching() { |
---|
1626 | std::vector<int> blossoms; |
---|
1627 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
1628 | blossoms.push_back(c); |
---|
1629 | } |
---|
1630 | |
---|
1631 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
1632 | if ((*_blossom_data)[blossoms[i]].status == MATCHED) { |
---|
1633 | |
---|
1634 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
1635 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
1636 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
1637 | n != INVALID; ++n) { |
---|
1638 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
1639 | } |
---|
1640 | |
---|
1641 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
1642 | Node base = _graph.source(matching); |
---|
1643 | extractBlossom(blossoms[i], base, matching); |
---|
1644 | } else { |
---|
1645 | Node base = (*_blossom_data)[blossoms[i]].base; |
---|
1646 | extractBlossom(blossoms[i], base, INVALID); |
---|
1647 | } |
---|
1648 | } |
---|
1649 | } |
---|
1650 | |
---|
1651 | public: |
---|
1652 | |
---|
1653 | /// \brief Constructor |
---|
1654 | /// |
---|
1655 | /// Constructor. |
---|
1656 | MaxWeightedMatching(const Graph& graph, const WeightMap& weight) |
---|
1657 | : _graph(graph), _weight(weight), _matching(0), |
---|
1658 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
1659 | _node_num(0), _blossom_num(0), |
---|
1660 | |
---|
1661 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
1662 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
1663 | _tree_set_index(0), _tree_set(0), |
---|
1664 | |
---|
1665 | _delta1_index(0), _delta1(0), |
---|
1666 | _delta2_index(0), _delta2(0), |
---|
1667 | _delta3_index(0), _delta3(0), |
---|
1668 | _delta4_index(0), _delta4(0), |
---|
1669 | |
---|
1670 | _delta_sum() {} |
---|
1671 | |
---|
1672 | ~MaxWeightedMatching() { |
---|
1673 | destroyStructures(); |
---|
1674 | } |
---|
1675 | |
---|
1676 | /// \name Execution Control |
---|
1677 | /// The simplest way to execute the algorithm is to use the |
---|
1678 | /// \ref run() member function. |
---|
1679 | |
---|
1680 | ///@{ |
---|
1681 | |
---|
1682 | /// \brief Initialize the algorithm |
---|
1683 | /// |
---|
1684 | /// This function initializes the algorithm. |
---|
1685 | void init() { |
---|
1686 | createStructures(); |
---|
1687 | |
---|
1688 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
1689 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
1690 | } |
---|
1691 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
1692 | (*_delta1_index)[n] = _delta1->PRE_HEAP; |
---|
1693 | } |
---|
1694 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
1695 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
1696 | } |
---|
1697 | for (int i = 0; i < _blossom_num; ++i) { |
---|
1698 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
1699 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
1700 | } |
---|
1701 | |
---|
1702 | int index = 0; |
---|
1703 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
1704 | Value max = 0; |
---|
1705 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
1706 | if (_graph.target(e) == n) continue; |
---|
1707 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
1708 | max = (dualScale * _weight[e]) / 2; |
---|
1709 | } |
---|
1710 | } |
---|
1711 | (*_node_index)[n] = index; |
---|
1712 | (*_node_data)[index].pot = max; |
---|
1713 | _delta1->push(n, max); |
---|
1714 | int blossom = |
---|
1715 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
1716 | |
---|
1717 | _tree_set->insert(blossom); |
---|
1718 | |
---|
1719 | (*_blossom_data)[blossom].status = EVEN; |
---|
1720 | (*_blossom_data)[blossom].pred = INVALID; |
---|
1721 | (*_blossom_data)[blossom].next = INVALID; |
---|
1722 | (*_blossom_data)[blossom].pot = 0; |
---|
1723 | (*_blossom_data)[blossom].offset = 0; |
---|
1724 | ++index; |
---|
1725 | } |
---|
1726 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
1727 | int si = (*_node_index)[_graph.u(e)]; |
---|
1728 | int ti = (*_node_index)[_graph.v(e)]; |
---|
1729 | if (_graph.u(e) != _graph.v(e)) { |
---|
1730 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
1731 | dualScale * _weight[e]) / 2); |
---|
1732 | } |
---|
1733 | } |
---|
1734 | } |
---|
1735 | |
---|
1736 | /// \brief Start the algorithm |
---|
1737 | /// |
---|
1738 | /// This function starts the algorithm. |
---|
1739 | /// |
---|
1740 | /// \pre \ref init() must be called before using this function. |
---|
1741 | void start() { |
---|
1742 | enum OpType { |
---|
1743 | D1, D2, D3, D4 |
---|
1744 | }; |
---|
1745 | |
---|
1746 | int unmatched = _node_num; |
---|
1747 | while (unmatched > 0) { |
---|
1748 | Value d1 = !_delta1->empty() ? |
---|
1749 | _delta1->prio() : std::numeric_limits<Value>::max(); |
---|
1750 | |
---|
1751 | Value d2 = !_delta2->empty() ? |
---|
1752 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
1753 | |
---|
1754 | Value d3 = !_delta3->empty() ? |
---|
1755 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
1756 | |
---|
1757 | Value d4 = !_delta4->empty() ? |
---|
1758 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
1759 | |
---|
1760 | _delta_sum = d1; OpType ot = D1; |
---|
1761 | if (d2 < _delta_sum) { _delta_sum = d2; ot = D2; } |
---|
1762 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
1763 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
1764 | |
---|
1765 | |
---|
1766 | switch (ot) { |
---|
1767 | case D1: |
---|
1768 | { |
---|
1769 | Node n = _delta1->top(); |
---|
1770 | unmatchNode(n); |
---|
1771 | --unmatched; |
---|
1772 | } |
---|
1773 | break; |
---|
1774 | case D2: |
---|
1775 | { |
---|
1776 | int blossom = _delta2->top(); |
---|
1777 | Node n = _blossom_set->classTop(blossom); |
---|
1778 | Arc e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
1779 | extendOnArc(e); |
---|
1780 | } |
---|
1781 | break; |
---|
1782 | case D3: |
---|
1783 | { |
---|
1784 | Edge e = _delta3->top(); |
---|
1785 | |
---|
1786 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
1787 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
1788 | |
---|
1789 | if (left_blossom == right_blossom) { |
---|
1790 | _delta3->pop(); |
---|
1791 | } else { |
---|
1792 | int left_tree; |
---|
1793 | if ((*_blossom_data)[left_blossom].status == EVEN) { |
---|
1794 | left_tree = _tree_set->find(left_blossom); |
---|
1795 | } else { |
---|
1796 | left_tree = -1; |
---|
1797 | ++unmatched; |
---|
1798 | } |
---|
1799 | int right_tree; |
---|
1800 | if ((*_blossom_data)[right_blossom].status == EVEN) { |
---|
1801 | right_tree = _tree_set->find(right_blossom); |
---|
1802 | } else { |
---|
1803 | right_tree = -1; |
---|
1804 | ++unmatched; |
---|
1805 | } |
---|
1806 | |
---|
1807 | if (left_tree == right_tree) { |
---|
1808 | shrinkOnEdge(e, left_tree); |
---|
1809 | } else { |
---|
1810 | augmentOnEdge(e); |
---|
1811 | unmatched -= 2; |
---|
1812 | } |
---|
1813 | } |
---|
1814 | } break; |
---|
1815 | case D4: |
---|
1816 | splitBlossom(_delta4->top()); |
---|
1817 | break; |
---|
1818 | } |
---|
1819 | } |
---|
1820 | extractMatching(); |
---|
1821 | } |
---|
1822 | |
---|
1823 | /// \brief Run the algorithm. |
---|
1824 | /// |
---|
1825 | /// This method runs the \c %MaxWeightedMatching algorithm. |
---|
1826 | /// |
---|
1827 | /// \note mwm.run() is just a shortcut of the following code. |
---|
1828 | /// \code |
---|
1829 | /// mwm.init(); |
---|
1830 | /// mwm.start(); |
---|
1831 | /// \endcode |
---|
1832 | void run() { |
---|
1833 | init(); |
---|
1834 | start(); |
---|
1835 | } |
---|
1836 | |
---|
1837 | /// @} |
---|
1838 | |
---|
1839 | /// \name Primal Solution |
---|
1840 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
1841 | /// matching.\n |
---|
1842 | /// Either \ref run() or \ref start() function should be called before |
---|
1843 | /// using them. |
---|
1844 | |
---|
1845 | /// @{ |
---|
1846 | |
---|
1847 | /// \brief Return the weight of the matching. |
---|
1848 | /// |
---|
1849 | /// This function returns the weight of the found matching. |
---|
1850 | /// |
---|
1851 | /// \pre Either run() or start() must be called before using this function. |
---|
1852 | Value matchingWeight() const { |
---|
1853 | Value sum = 0; |
---|
1854 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
1855 | if ((*_matching)[n] != INVALID) { |
---|
1856 | sum += _weight[(*_matching)[n]]; |
---|
1857 | } |
---|
1858 | } |
---|
1859 | return sum /= 2; |
---|
1860 | } |
---|
1861 | |
---|
1862 | /// \brief Return the size (cardinality) of the matching. |
---|
1863 | /// |
---|
1864 | /// This function returns the size (cardinality) of the found matching. |
---|
1865 | /// |
---|
1866 | /// \pre Either run() or start() must be called before using this function. |
---|
1867 | int matchingSize() const { |
---|
1868 | int num = 0; |
---|
1869 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
1870 | if ((*_matching)[n] != INVALID) { |
---|
1871 | ++num; |
---|
1872 | } |
---|
1873 | } |
---|
1874 | return num /= 2; |
---|
1875 | } |
---|
1876 | |
---|
1877 | /// \brief Return \c true if the given edge is in the matching. |
---|
1878 | /// |
---|
1879 | /// This function returns \c true if the given edge is in the found |
---|
1880 | /// matching. |
---|
1881 | /// |
---|
1882 | /// \pre Either run() or start() must be called before using this function. |
---|
1883 | bool matching(const Edge& edge) const { |
---|
1884 | return edge == (*_matching)[_graph.u(edge)]; |
---|
1885 | } |
---|
1886 | |
---|
1887 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
1888 | /// |
---|
1889 | /// This function returns the matching arc (or edge) incident to the |
---|
1890 | /// given node in the found matching or \c INVALID if the node is |
---|
1891 | /// not covered by the matching. |
---|
1892 | /// |
---|
1893 | /// \pre Either run() or start() must be called before using this function. |
---|
1894 | Arc matching(const Node& node) const { |
---|
1895 | return (*_matching)[node]; |
---|
1896 | } |
---|
1897 | |
---|
1898 | /// \brief Return a const reference to the matching map. |
---|
1899 | /// |
---|
1900 | /// This function returns a const reference to a node map that stores |
---|
1901 | /// the matching arc (or edge) incident to each node. |
---|
1902 | const MatchingMap& matchingMap() const { |
---|
1903 | return *_matching; |
---|
1904 | } |
---|
1905 | |
---|
1906 | /// \brief Return the mate of the given node. |
---|
1907 | /// |
---|
1908 | /// This function returns the mate of the given node in the found |
---|
1909 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
1910 | /// |
---|
1911 | /// \pre Either run() or start() must be called before using this function. |
---|
1912 | Node mate(const Node& node) const { |
---|
1913 | return (*_matching)[node] != INVALID ? |
---|
1914 | _graph.target((*_matching)[node]) : INVALID; |
---|
1915 | } |
---|
1916 | |
---|
1917 | /// @} |
---|
1918 | |
---|
1919 | /// \name Dual Solution |
---|
1920 | /// Functions to get the dual solution.\n |
---|
1921 | /// Either \ref run() or \ref start() function should be called before |
---|
1922 | /// using them. |
---|
1923 | |
---|
1924 | /// @{ |
---|
1925 | |
---|
1926 | /// \brief Return the value of the dual solution. |
---|
1927 | /// |
---|
1928 | /// This function returns the value of the dual solution. |
---|
1929 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
1930 | /// "dual scale". |
---|
1931 | /// |
---|
1932 | /// \pre Either run() or start() must be called before using this function. |
---|
1933 | Value dualValue() const { |
---|
1934 | Value sum = 0; |
---|
1935 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
1936 | sum += nodeValue(n); |
---|
1937 | } |
---|
1938 | for (int i = 0; i < blossomNum(); ++i) { |
---|
1939 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
1940 | } |
---|
1941 | return sum; |
---|
1942 | } |
---|
1943 | |
---|
1944 | /// \brief Return the dual value (potential) of the given node. |
---|
1945 | /// |
---|
1946 | /// This function returns the dual value (potential) of the given node. |
---|
1947 | /// |
---|
1948 | /// \pre Either run() or start() must be called before using this function. |
---|
1949 | Value nodeValue(const Node& n) const { |
---|
1950 | return (*_node_potential)[n]; |
---|
1951 | } |
---|
1952 | |
---|
1953 | /// \brief Return the number of the blossoms in the basis. |
---|
1954 | /// |
---|
1955 | /// This function returns the number of the blossoms in the basis. |
---|
1956 | /// |
---|
1957 | /// \pre Either run() or start() must be called before using this function. |
---|
1958 | /// \see BlossomIt |
---|
1959 | int blossomNum() const { |
---|
1960 | return _blossom_potential.size(); |
---|
1961 | } |
---|
1962 | |
---|
1963 | /// \brief Return the number of the nodes in the given blossom. |
---|
1964 | /// |
---|
1965 | /// This function returns the number of the nodes in the given blossom. |
---|
1966 | /// |
---|
1967 | /// \pre Either run() or start() must be called before using this function. |
---|
1968 | /// \see BlossomIt |
---|
1969 | int blossomSize(int k) const { |
---|
1970 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
1971 | } |
---|
1972 | |
---|
1973 | /// \brief Return the dual value (ptential) of the given blossom. |
---|
1974 | /// |
---|
1975 | /// This function returns the dual value (ptential) of the given blossom. |
---|
1976 | /// |
---|
1977 | /// \pre Either run() or start() must be called before using this function. |
---|
1978 | Value blossomValue(int k) const { |
---|
1979 | return _blossom_potential[k].value; |
---|
1980 | } |
---|
1981 | |
---|
1982 | /// \brief Iterator for obtaining the nodes of a blossom. |
---|
1983 | /// |
---|
1984 | /// This class provides an iterator for obtaining the nodes of the |
---|
1985 | /// given blossom. It lists a subset of the nodes. |
---|
1986 | /// Before using this iterator, you must allocate a |
---|
1987 | /// MaxWeightedMatching class and execute it. |
---|
1988 | class BlossomIt { |
---|
1989 | public: |
---|
1990 | |
---|
1991 | /// \brief Constructor. |
---|
1992 | /// |
---|
1993 | /// Constructor to get the nodes of the given variable. |
---|
1994 | /// |
---|
1995 | /// \pre Either \ref MaxWeightedMatching::run() "algorithm.run()" or |
---|
1996 | /// \ref MaxWeightedMatching::start() "algorithm.start()" must be |
---|
1997 | /// called before initializing this iterator. |
---|
1998 | BlossomIt(const MaxWeightedMatching& algorithm, int variable) |
---|
1999 | : _algorithm(&algorithm) |
---|
2000 | { |
---|
2001 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
2002 | _last = _algorithm->_blossom_potential[variable].end; |
---|
2003 | } |
---|
2004 | |
---|
2005 | /// \brief Conversion to \c Node. |
---|
2006 | /// |
---|
2007 | /// Conversion to \c Node. |
---|
2008 | operator Node() const { |
---|
2009 | return _algorithm->_blossom_node_list[_index]; |
---|
2010 | } |
---|
2011 | |
---|
2012 | /// \brief Increment operator. |
---|
2013 | /// |
---|
2014 | /// Increment operator. |
---|
2015 | BlossomIt& operator++() { |
---|
2016 | ++_index; |
---|
2017 | return *this; |
---|
2018 | } |
---|
2019 | |
---|
2020 | /// \brief Validity checking |
---|
2021 | /// |
---|
2022 | /// Checks whether the iterator is invalid. |
---|
2023 | bool operator==(Invalid) const { return _index == _last; } |
---|
2024 | |
---|
2025 | /// \brief Validity checking |
---|
2026 | /// |
---|
2027 | /// Checks whether the iterator is valid. |
---|
2028 | bool operator!=(Invalid) const { return _index != _last; } |
---|
2029 | |
---|
2030 | private: |
---|
2031 | const MaxWeightedMatching* _algorithm; |
---|
2032 | int _last; |
---|
2033 | int _index; |
---|
2034 | }; |
---|
2035 | |
---|
2036 | /// @} |
---|
2037 | |
---|
2038 | }; |
---|
2039 | |
---|
2040 | /// \ingroup matching |
---|
2041 | /// |
---|
2042 | /// \brief Weighted perfect matching in general graphs |
---|
2043 | /// |
---|
2044 | /// This class provides an efficient implementation of Edmond's |
---|
2045 | /// maximum weighted perfect matching algorithm. The implementation |
---|
2046 | /// is based on extensive use of priority queues and provides |
---|
2047 | /// \f$O(nm\log n)\f$ time complexity. |
---|
2048 | /// |
---|
2049 | /// The maximum weighted perfect matching problem is to find a subset of |
---|
2050 | /// the edges in an undirected graph with maximum overall weight for which |
---|
2051 | /// each node has exactly one incident edge. |
---|
2052 | /// It can be formulated with the following linear program. |
---|
2053 | /// \f[ \sum_{e \in \delta(u)}x_e = 1 \quad \forall u\in V\f] |
---|
2054 | /** \f[ \sum_{e \in \gamma(B)}x_e \le \frac{\vert B \vert - 1}{2} |
---|
2055 | \quad \forall B\in\mathcal{O}\f] */ |
---|
2056 | /// \f[x_e \ge 0\quad \forall e\in E\f] |
---|
2057 | /// \f[\max \sum_{e\in E}x_ew_e\f] |
---|
2058 | /// where \f$\delta(X)\f$ is the set of edges incident to a node in |
---|
2059 | /// \f$X\f$, \f$\gamma(X)\f$ is the set of edges with both ends in |
---|
2060 | /// \f$X\f$ and \f$\mathcal{O}\f$ is the set of odd cardinality |
---|
2061 | /// subsets of the nodes. |
---|
2062 | /// |
---|
2063 | /// The algorithm calculates an optimal matching and a proof of the |
---|
2064 | /// optimality. The solution of the dual problem can be used to check |
---|
2065 | /// the result of the algorithm. The dual linear problem is the |
---|
2066 | /// following. |
---|
2067 | /** \f[ y_u + y_v + \sum_{B \in \mathcal{O}, uv \in \gamma(B)}z_B \ge |
---|
2068 | w_{uv} \quad \forall uv\in E\f] */ |
---|
2069 | /// \f[z_B \ge 0 \quad \forall B \in \mathcal{O}\f] |
---|
2070 | /** \f[\min \sum_{u \in V}y_u + \sum_{B \in \mathcal{O}} |
---|
2071 | \frac{\vert B \vert - 1}{2}z_B\f] */ |
---|
2072 | /// |
---|
2073 | /// The algorithm can be executed with the run() function. |
---|
2074 | /// After it the matching (the primal solution) and the dual solution |
---|
2075 | /// can be obtained using the query functions and the |
---|
2076 | /// \ref MaxWeightedPerfectMatching::BlossomIt "BlossomIt" nested class, |
---|
2077 | /// which is able to iterate on the nodes of a blossom. |
---|
2078 | /// If the value type is integer, then the dual solution is multiplied |
---|
2079 | /// by \ref MaxWeightedMatching::dualScale "4". |
---|
2080 | /// |
---|
2081 | /// \tparam GR The undirected graph type the algorithm runs on. |
---|
2082 | /// \tparam WM The type edge weight map. The default type is |
---|
2083 | /// \ref concepts::Graph::EdgeMap "GR::EdgeMap<int>". |
---|
2084 | #ifdef DOXYGEN |
---|
2085 | template <typename GR, typename WM> |
---|
2086 | #else |
---|
2087 | template <typename GR, |
---|
2088 | typename WM = typename GR::template EdgeMap<int> > |
---|
2089 | #endif |
---|
2090 | class MaxWeightedPerfectMatching { |
---|
2091 | public: |
---|
2092 | |
---|
2093 | /// The graph type of the algorithm |
---|
2094 | typedef GR Graph; |
---|
2095 | /// The type of the edge weight map |
---|
2096 | typedef WM WeightMap; |
---|
2097 | /// The value type of the edge weights |
---|
2098 | typedef typename WeightMap::Value Value; |
---|
2099 | |
---|
2100 | /// \brief Scaling factor for dual solution |
---|
2101 | /// |
---|
2102 | /// Scaling factor for dual solution, it is equal to 4 or 1 |
---|
2103 | /// according to the value type. |
---|
2104 | static const int dualScale = |
---|
2105 | std::numeric_limits<Value>::is_integer ? 4 : 1; |
---|
2106 | |
---|
2107 | /// The type of the matching map |
---|
2108 | typedef typename Graph::template NodeMap<typename Graph::Arc> |
---|
2109 | MatchingMap; |
---|
2110 | |
---|
2111 | private: |
---|
2112 | |
---|
2113 | TEMPLATE_GRAPH_TYPEDEFS(Graph); |
---|
2114 | |
---|
2115 | typedef typename Graph::template NodeMap<Value> NodePotential; |
---|
2116 | typedef std::vector<Node> BlossomNodeList; |
---|
2117 | |
---|
2118 | struct BlossomVariable { |
---|
2119 | int begin, end; |
---|
2120 | Value value; |
---|
2121 | |
---|
2122 | BlossomVariable(int _begin, int _end, Value _value) |
---|
2123 | : begin(_begin), end(_end), value(_value) {} |
---|
2124 | |
---|
2125 | }; |
---|
2126 | |
---|
2127 | typedef std::vector<BlossomVariable> BlossomPotential; |
---|
2128 | |
---|
2129 | const Graph& _graph; |
---|
2130 | const WeightMap& _weight; |
---|
2131 | |
---|
2132 | MatchingMap* _matching; |
---|
2133 | |
---|
2134 | NodePotential* _node_potential; |
---|
2135 | |
---|
2136 | BlossomPotential _blossom_potential; |
---|
2137 | BlossomNodeList _blossom_node_list; |
---|
2138 | |
---|
2139 | int _node_num; |
---|
2140 | int _blossom_num; |
---|
2141 | |
---|
2142 | typedef RangeMap<int> IntIntMap; |
---|
2143 | |
---|
2144 | enum Status { |
---|
2145 | EVEN = -1, MATCHED = 0, ODD = 1 |
---|
2146 | }; |
---|
2147 | |
---|
2148 | typedef HeapUnionFind<Value, IntNodeMap> BlossomSet; |
---|
2149 | struct BlossomData { |
---|
2150 | int tree; |
---|
2151 | Status status; |
---|
2152 | Arc pred, next; |
---|
2153 | Value pot, offset; |
---|
2154 | }; |
---|
2155 | |
---|
2156 | IntNodeMap *_blossom_index; |
---|
2157 | BlossomSet *_blossom_set; |
---|
2158 | RangeMap<BlossomData>* _blossom_data; |
---|
2159 | |
---|
2160 | IntNodeMap *_node_index; |
---|
2161 | IntArcMap *_node_heap_index; |
---|
2162 | |
---|
2163 | struct NodeData { |
---|
2164 | |
---|
2165 | NodeData(IntArcMap& node_heap_index) |
---|
2166 | : heap(node_heap_index) {} |
---|
2167 | |
---|
2168 | int blossom; |
---|
2169 | Value pot; |
---|
2170 | BinHeap<Value, IntArcMap> heap; |
---|
2171 | std::map<int, Arc> heap_index; |
---|
2172 | |
---|
2173 | int tree; |
---|
2174 | }; |
---|
2175 | |
---|
2176 | RangeMap<NodeData>* _node_data; |
---|
2177 | |
---|
2178 | typedef ExtendFindEnum<IntIntMap> TreeSet; |
---|
2179 | |
---|
2180 | IntIntMap *_tree_set_index; |
---|
2181 | TreeSet *_tree_set; |
---|
2182 | |
---|
2183 | IntIntMap *_delta2_index; |
---|
2184 | BinHeap<Value, IntIntMap> *_delta2; |
---|
2185 | |
---|
2186 | IntEdgeMap *_delta3_index; |
---|
2187 | BinHeap<Value, IntEdgeMap> *_delta3; |
---|
2188 | |
---|
2189 | IntIntMap *_delta4_index; |
---|
2190 | BinHeap<Value, IntIntMap> *_delta4; |
---|
2191 | |
---|
2192 | Value _delta_sum; |
---|
2193 | |
---|
2194 | void createStructures() { |
---|
2195 | _node_num = countNodes(_graph); |
---|
2196 | _blossom_num = _node_num * 3 / 2; |
---|
2197 | |
---|
2198 | if (!_matching) { |
---|
2199 | _matching = new MatchingMap(_graph); |
---|
2200 | } |
---|
2201 | if (!_node_potential) { |
---|
2202 | _node_potential = new NodePotential(_graph); |
---|
2203 | } |
---|
2204 | if (!_blossom_set) { |
---|
2205 | _blossom_index = new IntNodeMap(_graph); |
---|
2206 | _blossom_set = new BlossomSet(*_blossom_index); |
---|
2207 | _blossom_data = new RangeMap<BlossomData>(_blossom_num); |
---|
2208 | } |
---|
2209 | |
---|
2210 | if (!_node_index) { |
---|
2211 | _node_index = new IntNodeMap(_graph); |
---|
2212 | _node_heap_index = new IntArcMap(_graph); |
---|
2213 | _node_data = new RangeMap<NodeData>(_node_num, |
---|
2214 | NodeData(*_node_heap_index)); |
---|
2215 | } |
---|
2216 | |
---|
2217 | if (!_tree_set) { |
---|
2218 | _tree_set_index = new IntIntMap(_blossom_num); |
---|
2219 | _tree_set = new TreeSet(*_tree_set_index); |
---|
2220 | } |
---|
2221 | if (!_delta2) { |
---|
2222 | _delta2_index = new IntIntMap(_blossom_num); |
---|
2223 | _delta2 = new BinHeap<Value, IntIntMap>(*_delta2_index); |
---|
2224 | } |
---|
2225 | if (!_delta3) { |
---|
2226 | _delta3_index = new IntEdgeMap(_graph); |
---|
2227 | _delta3 = new BinHeap<Value, IntEdgeMap>(*_delta3_index); |
---|
2228 | } |
---|
2229 | if (!_delta4) { |
---|
2230 | _delta4_index = new IntIntMap(_blossom_num); |
---|
2231 | _delta4 = new BinHeap<Value, IntIntMap>(*_delta4_index); |
---|
2232 | } |
---|
2233 | } |
---|
2234 | |
---|
2235 | void destroyStructures() { |
---|
2236 | _node_num = countNodes(_graph); |
---|
2237 | _blossom_num = _node_num * 3 / 2; |
---|
2238 | |
---|
2239 | if (_matching) { |
---|
2240 | delete _matching; |
---|
2241 | } |
---|
2242 | if (_node_potential) { |
---|
2243 | delete _node_potential; |
---|
2244 | } |
---|
2245 | if (_blossom_set) { |
---|
2246 | delete _blossom_index; |
---|
2247 | delete _blossom_set; |
---|
2248 | delete _blossom_data; |
---|
2249 | } |
---|
2250 | |
---|
2251 | if (_node_index) { |
---|
2252 | delete _node_index; |
---|
2253 | delete _node_heap_index; |
---|
2254 | delete _node_data; |
---|
2255 | } |
---|
2256 | |
---|
2257 | if (_tree_set) { |
---|
2258 | delete _tree_set_index; |
---|
2259 | delete _tree_set; |
---|
2260 | } |
---|
2261 | if (_delta2) { |
---|
2262 | delete _delta2_index; |
---|
2263 | delete _delta2; |
---|
2264 | } |
---|
2265 | if (_delta3) { |
---|
2266 | delete _delta3_index; |
---|
2267 | delete _delta3; |
---|
2268 | } |
---|
2269 | if (_delta4) { |
---|
2270 | delete _delta4_index; |
---|
2271 | delete _delta4; |
---|
2272 | } |
---|
2273 | } |
---|
2274 | |
---|
2275 | void matchedToEven(int blossom, int tree) { |
---|
2276 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
2277 | _delta2->erase(blossom); |
---|
2278 | } |
---|
2279 | |
---|
2280 | if (!_blossom_set->trivial(blossom)) { |
---|
2281 | (*_blossom_data)[blossom].pot -= |
---|
2282 | 2 * (_delta_sum - (*_blossom_data)[blossom].offset); |
---|
2283 | } |
---|
2284 | |
---|
2285 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
2286 | n != INVALID; ++n) { |
---|
2287 | |
---|
2288 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
2289 | int ni = (*_node_index)[n]; |
---|
2290 | |
---|
2291 | (*_node_data)[ni].heap.clear(); |
---|
2292 | (*_node_data)[ni].heap_index.clear(); |
---|
2293 | |
---|
2294 | (*_node_data)[ni].pot += _delta_sum - (*_blossom_data)[blossom].offset; |
---|
2295 | |
---|
2296 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
2297 | Node v = _graph.source(e); |
---|
2298 | int vb = _blossom_set->find(v); |
---|
2299 | int vi = (*_node_index)[v]; |
---|
2300 | |
---|
2301 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
2302 | dualScale * _weight[e]; |
---|
2303 | |
---|
2304 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
2305 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
2306 | _delta3->push(e, rw / 2); |
---|
2307 | } |
---|
2308 | } else { |
---|
2309 | typename std::map<int, Arc>::iterator it = |
---|
2310 | (*_node_data)[vi].heap_index.find(tree); |
---|
2311 | |
---|
2312 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
2313 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
2314 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
2315 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
2316 | it->second = e; |
---|
2317 | } |
---|
2318 | } else { |
---|
2319 | (*_node_data)[vi].heap.push(e, rw); |
---|
2320 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
2321 | } |
---|
2322 | |
---|
2323 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
2324 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
2325 | |
---|
2326 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
2327 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
2328 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
2329 | (*_blossom_data)[vb].offset); |
---|
2330 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
2331 | (*_blossom_data)[vb].offset){ |
---|
2332 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
2333 | (*_blossom_data)[vb].offset); |
---|
2334 | } |
---|
2335 | } |
---|
2336 | } |
---|
2337 | } |
---|
2338 | } |
---|
2339 | } |
---|
2340 | (*_blossom_data)[blossom].offset = 0; |
---|
2341 | } |
---|
2342 | |
---|
2343 | void matchedToOdd(int blossom) { |
---|
2344 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
2345 | _delta2->erase(blossom); |
---|
2346 | } |
---|
2347 | (*_blossom_data)[blossom].offset += _delta_sum; |
---|
2348 | if (!_blossom_set->trivial(blossom)) { |
---|
2349 | _delta4->push(blossom, (*_blossom_data)[blossom].pot / 2 + |
---|
2350 | (*_blossom_data)[blossom].offset); |
---|
2351 | } |
---|
2352 | } |
---|
2353 | |
---|
2354 | void evenToMatched(int blossom, int tree) { |
---|
2355 | if (!_blossom_set->trivial(blossom)) { |
---|
2356 | (*_blossom_data)[blossom].pot += 2 * _delta_sum; |
---|
2357 | } |
---|
2358 | |
---|
2359 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
2360 | n != INVALID; ++n) { |
---|
2361 | int ni = (*_node_index)[n]; |
---|
2362 | (*_node_data)[ni].pot -= _delta_sum; |
---|
2363 | |
---|
2364 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
2365 | Node v = _graph.source(e); |
---|
2366 | int vb = _blossom_set->find(v); |
---|
2367 | int vi = (*_node_index)[v]; |
---|
2368 | |
---|
2369 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
2370 | dualScale * _weight[e]; |
---|
2371 | |
---|
2372 | if (vb == blossom) { |
---|
2373 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
2374 | _delta3->erase(e); |
---|
2375 | } |
---|
2376 | } else if ((*_blossom_data)[vb].status == EVEN) { |
---|
2377 | |
---|
2378 | if (_delta3->state(e) == _delta3->IN_HEAP) { |
---|
2379 | _delta3->erase(e); |
---|
2380 | } |
---|
2381 | |
---|
2382 | int vt = _tree_set->find(vb); |
---|
2383 | |
---|
2384 | if (vt != tree) { |
---|
2385 | |
---|
2386 | Arc r = _graph.oppositeArc(e); |
---|
2387 | |
---|
2388 | typename std::map<int, Arc>::iterator it = |
---|
2389 | (*_node_data)[ni].heap_index.find(vt); |
---|
2390 | |
---|
2391 | if (it != (*_node_data)[ni].heap_index.end()) { |
---|
2392 | if ((*_node_data)[ni].heap[it->second] > rw) { |
---|
2393 | (*_node_data)[ni].heap.replace(it->second, r); |
---|
2394 | (*_node_data)[ni].heap.decrease(r, rw); |
---|
2395 | it->second = r; |
---|
2396 | } |
---|
2397 | } else { |
---|
2398 | (*_node_data)[ni].heap.push(r, rw); |
---|
2399 | (*_node_data)[ni].heap_index.insert(std::make_pair(vt, r)); |
---|
2400 | } |
---|
2401 | |
---|
2402 | if ((*_blossom_set)[n] > (*_node_data)[ni].heap.prio()) { |
---|
2403 | _blossom_set->decrease(n, (*_node_data)[ni].heap.prio()); |
---|
2404 | |
---|
2405 | if (_delta2->state(blossom) != _delta2->IN_HEAP) { |
---|
2406 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
2407 | (*_blossom_data)[blossom].offset); |
---|
2408 | } else if ((*_delta2)[blossom] > |
---|
2409 | _blossom_set->classPrio(blossom) - |
---|
2410 | (*_blossom_data)[blossom].offset){ |
---|
2411 | _delta2->decrease(blossom, _blossom_set->classPrio(blossom) - |
---|
2412 | (*_blossom_data)[blossom].offset); |
---|
2413 | } |
---|
2414 | } |
---|
2415 | } |
---|
2416 | } else { |
---|
2417 | |
---|
2418 | typename std::map<int, Arc>::iterator it = |
---|
2419 | (*_node_data)[vi].heap_index.find(tree); |
---|
2420 | |
---|
2421 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
2422 | (*_node_data)[vi].heap.erase(it->second); |
---|
2423 | (*_node_data)[vi].heap_index.erase(it); |
---|
2424 | if ((*_node_data)[vi].heap.empty()) { |
---|
2425 | _blossom_set->increase(v, std::numeric_limits<Value>::max()); |
---|
2426 | } else if ((*_blossom_set)[v] < (*_node_data)[vi].heap.prio()) { |
---|
2427 | _blossom_set->increase(v, (*_node_data)[vi].heap.prio()); |
---|
2428 | } |
---|
2429 | |
---|
2430 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
2431 | if (_blossom_set->classPrio(vb) == |
---|
2432 | std::numeric_limits<Value>::max()) { |
---|
2433 | _delta2->erase(vb); |
---|
2434 | } else if ((*_delta2)[vb] < _blossom_set->classPrio(vb) - |
---|
2435 | (*_blossom_data)[vb].offset) { |
---|
2436 | _delta2->increase(vb, _blossom_set->classPrio(vb) - |
---|
2437 | (*_blossom_data)[vb].offset); |
---|
2438 | } |
---|
2439 | } |
---|
2440 | } |
---|
2441 | } |
---|
2442 | } |
---|
2443 | } |
---|
2444 | } |
---|
2445 | |
---|
2446 | void oddToMatched(int blossom) { |
---|
2447 | (*_blossom_data)[blossom].offset -= _delta_sum; |
---|
2448 | |
---|
2449 | if (_blossom_set->classPrio(blossom) != |
---|
2450 | std::numeric_limits<Value>::max()) { |
---|
2451 | _delta2->push(blossom, _blossom_set->classPrio(blossom) - |
---|
2452 | (*_blossom_data)[blossom].offset); |
---|
2453 | } |
---|
2454 | |
---|
2455 | if (!_blossom_set->trivial(blossom)) { |
---|
2456 | _delta4->erase(blossom); |
---|
2457 | } |
---|
2458 | } |
---|
2459 | |
---|
2460 | void oddToEven(int blossom, int tree) { |
---|
2461 | if (!_blossom_set->trivial(blossom)) { |
---|
2462 | _delta4->erase(blossom); |
---|
2463 | (*_blossom_data)[blossom].pot -= |
---|
2464 | 2 * (2 * _delta_sum - (*_blossom_data)[blossom].offset); |
---|
2465 | } |
---|
2466 | |
---|
2467 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossom); |
---|
2468 | n != INVALID; ++n) { |
---|
2469 | int ni = (*_node_index)[n]; |
---|
2470 | |
---|
2471 | _blossom_set->increase(n, std::numeric_limits<Value>::max()); |
---|
2472 | |
---|
2473 | (*_node_data)[ni].heap.clear(); |
---|
2474 | (*_node_data)[ni].heap_index.clear(); |
---|
2475 | (*_node_data)[ni].pot += |
---|
2476 | 2 * _delta_sum - (*_blossom_data)[blossom].offset; |
---|
2477 | |
---|
2478 | for (InArcIt e(_graph, n); e != INVALID; ++e) { |
---|
2479 | Node v = _graph.source(e); |
---|
2480 | int vb = _blossom_set->find(v); |
---|
2481 | int vi = (*_node_index)[v]; |
---|
2482 | |
---|
2483 | Value rw = (*_node_data)[ni].pot + (*_node_data)[vi].pot - |
---|
2484 | dualScale * _weight[e]; |
---|
2485 | |
---|
2486 | if ((*_blossom_data)[vb].status == EVEN) { |
---|
2487 | if (_delta3->state(e) != _delta3->IN_HEAP && blossom != vb) { |
---|
2488 | _delta3->push(e, rw / 2); |
---|
2489 | } |
---|
2490 | } else { |
---|
2491 | |
---|
2492 | typename std::map<int, Arc>::iterator it = |
---|
2493 | (*_node_data)[vi].heap_index.find(tree); |
---|
2494 | |
---|
2495 | if (it != (*_node_data)[vi].heap_index.end()) { |
---|
2496 | if ((*_node_data)[vi].heap[it->second] > rw) { |
---|
2497 | (*_node_data)[vi].heap.replace(it->second, e); |
---|
2498 | (*_node_data)[vi].heap.decrease(e, rw); |
---|
2499 | it->second = e; |
---|
2500 | } |
---|
2501 | } else { |
---|
2502 | (*_node_data)[vi].heap.push(e, rw); |
---|
2503 | (*_node_data)[vi].heap_index.insert(std::make_pair(tree, e)); |
---|
2504 | } |
---|
2505 | |
---|
2506 | if ((*_blossom_set)[v] > (*_node_data)[vi].heap.prio()) { |
---|
2507 | _blossom_set->decrease(v, (*_node_data)[vi].heap.prio()); |
---|
2508 | |
---|
2509 | if ((*_blossom_data)[vb].status == MATCHED) { |
---|
2510 | if (_delta2->state(vb) != _delta2->IN_HEAP) { |
---|
2511 | _delta2->push(vb, _blossom_set->classPrio(vb) - |
---|
2512 | (*_blossom_data)[vb].offset); |
---|
2513 | } else if ((*_delta2)[vb] > _blossom_set->classPrio(vb) - |
---|
2514 | (*_blossom_data)[vb].offset) { |
---|
2515 | _delta2->decrease(vb, _blossom_set->classPrio(vb) - |
---|
2516 | (*_blossom_data)[vb].offset); |
---|
2517 | } |
---|
2518 | } |
---|
2519 | } |
---|
2520 | } |
---|
2521 | } |
---|
2522 | } |
---|
2523 | (*_blossom_data)[blossom].offset = 0; |
---|
2524 | } |
---|
2525 | |
---|
2526 | void alternatePath(int even, int tree) { |
---|
2527 | int odd; |
---|
2528 | |
---|
2529 | evenToMatched(even, tree); |
---|
2530 | (*_blossom_data)[even].status = MATCHED; |
---|
2531 | |
---|
2532 | while ((*_blossom_data)[even].pred != INVALID) { |
---|
2533 | odd = _blossom_set->find(_graph.target((*_blossom_data)[even].pred)); |
---|
2534 | (*_blossom_data)[odd].status = MATCHED; |
---|
2535 | oddToMatched(odd); |
---|
2536 | (*_blossom_data)[odd].next = (*_blossom_data)[odd].pred; |
---|
2537 | |
---|
2538 | even = _blossom_set->find(_graph.target((*_blossom_data)[odd].pred)); |
---|
2539 | (*_blossom_data)[even].status = MATCHED; |
---|
2540 | evenToMatched(even, tree); |
---|
2541 | (*_blossom_data)[even].next = |
---|
2542 | _graph.oppositeArc((*_blossom_data)[odd].pred); |
---|
2543 | } |
---|
2544 | |
---|
2545 | } |
---|
2546 | |
---|
2547 | void destroyTree(int tree) { |
---|
2548 | for (TreeSet::ItemIt b(*_tree_set, tree); b != INVALID; ++b) { |
---|
2549 | if ((*_blossom_data)[b].status == EVEN) { |
---|
2550 | (*_blossom_data)[b].status = MATCHED; |
---|
2551 | evenToMatched(b, tree); |
---|
2552 | } else if ((*_blossom_data)[b].status == ODD) { |
---|
2553 | (*_blossom_data)[b].status = MATCHED; |
---|
2554 | oddToMatched(b); |
---|
2555 | } |
---|
2556 | } |
---|
2557 | _tree_set->eraseClass(tree); |
---|
2558 | } |
---|
2559 | |
---|
2560 | void augmentOnEdge(const Edge& edge) { |
---|
2561 | |
---|
2562 | int left = _blossom_set->find(_graph.u(edge)); |
---|
2563 | int right = _blossom_set->find(_graph.v(edge)); |
---|
2564 | |
---|
2565 | int left_tree = _tree_set->find(left); |
---|
2566 | alternatePath(left, left_tree); |
---|
2567 | destroyTree(left_tree); |
---|
2568 | |
---|
2569 | int right_tree = _tree_set->find(right); |
---|
2570 | alternatePath(right, right_tree); |
---|
2571 | destroyTree(right_tree); |
---|
2572 | |
---|
2573 | (*_blossom_data)[left].next = _graph.direct(edge, true); |
---|
2574 | (*_blossom_data)[right].next = _graph.direct(edge, false); |
---|
2575 | } |
---|
2576 | |
---|
2577 | void extendOnArc(const Arc& arc) { |
---|
2578 | int base = _blossom_set->find(_graph.target(arc)); |
---|
2579 | int tree = _tree_set->find(base); |
---|
2580 | |
---|
2581 | int odd = _blossom_set->find(_graph.source(arc)); |
---|
2582 | _tree_set->insert(odd, tree); |
---|
2583 | (*_blossom_data)[odd].status = ODD; |
---|
2584 | matchedToOdd(odd); |
---|
2585 | (*_blossom_data)[odd].pred = arc; |
---|
2586 | |
---|
2587 | int even = _blossom_set->find(_graph.target((*_blossom_data)[odd].next)); |
---|
2588 | (*_blossom_data)[even].pred = (*_blossom_data)[even].next; |
---|
2589 | _tree_set->insert(even, tree); |
---|
2590 | (*_blossom_data)[even].status = EVEN; |
---|
2591 | matchedToEven(even, tree); |
---|
2592 | } |
---|
2593 | |
---|
2594 | void shrinkOnEdge(const Edge& edge, int tree) { |
---|
2595 | int nca = -1; |
---|
2596 | std::vector<int> left_path, right_path; |
---|
2597 | |
---|
2598 | { |
---|
2599 | std::set<int> left_set, right_set; |
---|
2600 | int left = _blossom_set->find(_graph.u(edge)); |
---|
2601 | left_path.push_back(left); |
---|
2602 | left_set.insert(left); |
---|
2603 | |
---|
2604 | int right = _blossom_set->find(_graph.v(edge)); |
---|
2605 | right_path.push_back(right); |
---|
2606 | right_set.insert(right); |
---|
2607 | |
---|
2608 | while (true) { |
---|
2609 | |
---|
2610 | if ((*_blossom_data)[left].pred == INVALID) break; |
---|
2611 | |
---|
2612 | left = |
---|
2613 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
2614 | left_path.push_back(left); |
---|
2615 | left = |
---|
2616 | _blossom_set->find(_graph.target((*_blossom_data)[left].pred)); |
---|
2617 | left_path.push_back(left); |
---|
2618 | |
---|
2619 | left_set.insert(left); |
---|
2620 | |
---|
2621 | if (right_set.find(left) != right_set.end()) { |
---|
2622 | nca = left; |
---|
2623 | break; |
---|
2624 | } |
---|
2625 | |
---|
2626 | if ((*_blossom_data)[right].pred == INVALID) break; |
---|
2627 | |
---|
2628 | right = |
---|
2629 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
2630 | right_path.push_back(right); |
---|
2631 | right = |
---|
2632 | _blossom_set->find(_graph.target((*_blossom_data)[right].pred)); |
---|
2633 | right_path.push_back(right); |
---|
2634 | |
---|
2635 | right_set.insert(right); |
---|
2636 | |
---|
2637 | if (left_set.find(right) != left_set.end()) { |
---|
2638 | nca = right; |
---|
2639 | break; |
---|
2640 | } |
---|
2641 | |
---|
2642 | } |
---|
2643 | |
---|
2644 | if (nca == -1) { |
---|
2645 | if ((*_blossom_data)[left].pred == INVALID) { |
---|
2646 | nca = right; |
---|
2647 | while (left_set.find(nca) == left_set.end()) { |
---|
2648 | nca = |
---|
2649 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
2650 | right_path.push_back(nca); |
---|
2651 | nca = |
---|
2652 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
2653 | right_path.push_back(nca); |
---|
2654 | } |
---|
2655 | } else { |
---|
2656 | nca = left; |
---|
2657 | while (right_set.find(nca) == right_set.end()) { |
---|
2658 | nca = |
---|
2659 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
2660 | left_path.push_back(nca); |
---|
2661 | nca = |
---|
2662 | _blossom_set->find(_graph.target((*_blossom_data)[nca].pred)); |
---|
2663 | left_path.push_back(nca); |
---|
2664 | } |
---|
2665 | } |
---|
2666 | } |
---|
2667 | } |
---|
2668 | |
---|
2669 | std::vector<int> subblossoms; |
---|
2670 | Arc prev; |
---|
2671 | |
---|
2672 | prev = _graph.direct(edge, true); |
---|
2673 | for (int i = 0; left_path[i] != nca; i += 2) { |
---|
2674 | subblossoms.push_back(left_path[i]); |
---|
2675 | (*_blossom_data)[left_path[i]].next = prev; |
---|
2676 | _tree_set->erase(left_path[i]); |
---|
2677 | |
---|
2678 | subblossoms.push_back(left_path[i + 1]); |
---|
2679 | (*_blossom_data)[left_path[i + 1]].status = EVEN; |
---|
2680 | oddToEven(left_path[i + 1], tree); |
---|
2681 | _tree_set->erase(left_path[i + 1]); |
---|
2682 | prev = _graph.oppositeArc((*_blossom_data)[left_path[i + 1]].pred); |
---|
2683 | } |
---|
2684 | |
---|
2685 | int k = 0; |
---|
2686 | while (right_path[k] != nca) ++k; |
---|
2687 | |
---|
2688 | subblossoms.push_back(nca); |
---|
2689 | (*_blossom_data)[nca].next = prev; |
---|
2690 | |
---|
2691 | for (int i = k - 2; i >= 0; i -= 2) { |
---|
2692 | subblossoms.push_back(right_path[i + 1]); |
---|
2693 | (*_blossom_data)[right_path[i + 1]].status = EVEN; |
---|
2694 | oddToEven(right_path[i + 1], tree); |
---|
2695 | _tree_set->erase(right_path[i + 1]); |
---|
2696 | |
---|
2697 | (*_blossom_data)[right_path[i + 1]].next = |
---|
2698 | (*_blossom_data)[right_path[i + 1]].pred; |
---|
2699 | |
---|
2700 | subblossoms.push_back(right_path[i]); |
---|
2701 | _tree_set->erase(right_path[i]); |
---|
2702 | } |
---|
2703 | |
---|
2704 | int surface = |
---|
2705 | _blossom_set->join(subblossoms.begin(), subblossoms.end()); |
---|
2706 | |
---|
2707 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
2708 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
2709 | (*_blossom_data)[subblossoms[i]].pot += 2 * _delta_sum; |
---|
2710 | } |
---|
2711 | (*_blossom_data)[subblossoms[i]].status = MATCHED; |
---|
2712 | } |
---|
2713 | |
---|
2714 | (*_blossom_data)[surface].pot = -2 * _delta_sum; |
---|
2715 | (*_blossom_data)[surface].offset = 0; |
---|
2716 | (*_blossom_data)[surface].status = EVEN; |
---|
2717 | (*_blossom_data)[surface].pred = (*_blossom_data)[nca].pred; |
---|
2718 | (*_blossom_data)[surface].next = (*_blossom_data)[nca].pred; |
---|
2719 | |
---|
2720 | _tree_set->insert(surface, tree); |
---|
2721 | _tree_set->erase(nca); |
---|
2722 | } |
---|
2723 | |
---|
2724 | void splitBlossom(int blossom) { |
---|
2725 | Arc next = (*_blossom_data)[blossom].next; |
---|
2726 | Arc pred = (*_blossom_data)[blossom].pred; |
---|
2727 | |
---|
2728 | int tree = _tree_set->find(blossom); |
---|
2729 | |
---|
2730 | (*_blossom_data)[blossom].status = MATCHED; |
---|
2731 | oddToMatched(blossom); |
---|
2732 | if (_delta2->state(blossom) == _delta2->IN_HEAP) { |
---|
2733 | _delta2->erase(blossom); |
---|
2734 | } |
---|
2735 | |
---|
2736 | std::vector<int> subblossoms; |
---|
2737 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
2738 | |
---|
2739 | Value offset = (*_blossom_data)[blossom].offset; |
---|
2740 | int b = _blossom_set->find(_graph.source(pred)); |
---|
2741 | int d = _blossom_set->find(_graph.source(next)); |
---|
2742 | |
---|
2743 | int ib = -1, id = -1; |
---|
2744 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
2745 | if (subblossoms[i] == b) ib = i; |
---|
2746 | if (subblossoms[i] == d) id = i; |
---|
2747 | |
---|
2748 | (*_blossom_data)[subblossoms[i]].offset = offset; |
---|
2749 | if (!_blossom_set->trivial(subblossoms[i])) { |
---|
2750 | (*_blossom_data)[subblossoms[i]].pot -= 2 * offset; |
---|
2751 | } |
---|
2752 | if (_blossom_set->classPrio(subblossoms[i]) != |
---|
2753 | std::numeric_limits<Value>::max()) { |
---|
2754 | _delta2->push(subblossoms[i], |
---|
2755 | _blossom_set->classPrio(subblossoms[i]) - |
---|
2756 | (*_blossom_data)[subblossoms[i]].offset); |
---|
2757 | } |
---|
2758 | } |
---|
2759 | |
---|
2760 | if (id > ib ? ((id - ib) % 2 == 0) : ((ib - id) % 2 == 1)) { |
---|
2761 | for (int i = (id + 1) % subblossoms.size(); |
---|
2762 | i != ib; i = (i + 2) % subblossoms.size()) { |
---|
2763 | int sb = subblossoms[i]; |
---|
2764 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
2765 | (*_blossom_data)[sb].next = |
---|
2766 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
2767 | } |
---|
2768 | |
---|
2769 | for (int i = ib; i != id; i = (i + 2) % subblossoms.size()) { |
---|
2770 | int sb = subblossoms[i]; |
---|
2771 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
2772 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
2773 | |
---|
2774 | (*_blossom_data)[sb].status = ODD; |
---|
2775 | matchedToOdd(sb); |
---|
2776 | _tree_set->insert(sb, tree); |
---|
2777 | (*_blossom_data)[sb].pred = pred; |
---|
2778 | (*_blossom_data)[sb].next = |
---|
2779 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
2780 | |
---|
2781 | pred = (*_blossom_data)[ub].next; |
---|
2782 | |
---|
2783 | (*_blossom_data)[tb].status = EVEN; |
---|
2784 | matchedToEven(tb, tree); |
---|
2785 | _tree_set->insert(tb, tree); |
---|
2786 | (*_blossom_data)[tb].pred = (*_blossom_data)[tb].next; |
---|
2787 | } |
---|
2788 | |
---|
2789 | (*_blossom_data)[subblossoms[id]].status = ODD; |
---|
2790 | matchedToOdd(subblossoms[id]); |
---|
2791 | _tree_set->insert(subblossoms[id], tree); |
---|
2792 | (*_blossom_data)[subblossoms[id]].next = next; |
---|
2793 | (*_blossom_data)[subblossoms[id]].pred = pred; |
---|
2794 | |
---|
2795 | } else { |
---|
2796 | |
---|
2797 | for (int i = (ib + 1) % subblossoms.size(); |
---|
2798 | i != id; i = (i + 2) % subblossoms.size()) { |
---|
2799 | int sb = subblossoms[i]; |
---|
2800 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
2801 | (*_blossom_data)[sb].next = |
---|
2802 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
2803 | } |
---|
2804 | |
---|
2805 | for (int i = id; i != ib; i = (i + 2) % subblossoms.size()) { |
---|
2806 | int sb = subblossoms[i]; |
---|
2807 | int tb = subblossoms[(i + 1) % subblossoms.size()]; |
---|
2808 | int ub = subblossoms[(i + 2) % subblossoms.size()]; |
---|
2809 | |
---|
2810 | (*_blossom_data)[sb].status = ODD; |
---|
2811 | matchedToOdd(sb); |
---|
2812 | _tree_set->insert(sb, tree); |
---|
2813 | (*_blossom_data)[sb].next = next; |
---|
2814 | (*_blossom_data)[sb].pred = |
---|
2815 | _graph.oppositeArc((*_blossom_data)[tb].next); |
---|
2816 | |
---|
2817 | (*_blossom_data)[tb].status = EVEN; |
---|
2818 | matchedToEven(tb, tree); |
---|
2819 | _tree_set->insert(tb, tree); |
---|
2820 | (*_blossom_data)[tb].pred = |
---|
2821 | (*_blossom_data)[tb].next = |
---|
2822 | _graph.oppositeArc((*_blossom_data)[ub].next); |
---|
2823 | next = (*_blossom_data)[ub].next; |
---|
2824 | } |
---|
2825 | |
---|
2826 | (*_blossom_data)[subblossoms[ib]].status = ODD; |
---|
2827 | matchedToOdd(subblossoms[ib]); |
---|
2828 | _tree_set->insert(subblossoms[ib], tree); |
---|
2829 | (*_blossom_data)[subblossoms[ib]].next = next; |
---|
2830 | (*_blossom_data)[subblossoms[ib]].pred = pred; |
---|
2831 | } |
---|
2832 | _tree_set->erase(blossom); |
---|
2833 | } |
---|
2834 | |
---|
2835 | void extractBlossom(int blossom, const Node& base, const Arc& matching) { |
---|
2836 | if (_blossom_set->trivial(blossom)) { |
---|
2837 | int bi = (*_node_index)[base]; |
---|
2838 | Value pot = (*_node_data)[bi].pot; |
---|
2839 | |
---|
2840 | (*_matching)[base] = matching; |
---|
2841 | _blossom_node_list.push_back(base); |
---|
2842 | (*_node_potential)[base] = pot; |
---|
2843 | } else { |
---|
2844 | |
---|
2845 | Value pot = (*_blossom_data)[blossom].pot; |
---|
2846 | int bn = _blossom_node_list.size(); |
---|
2847 | |
---|
2848 | std::vector<int> subblossoms; |
---|
2849 | _blossom_set->split(blossom, std::back_inserter(subblossoms)); |
---|
2850 | int b = _blossom_set->find(base); |
---|
2851 | int ib = -1; |
---|
2852 | for (int i = 0; i < int(subblossoms.size()); ++i) { |
---|
2853 | if (subblossoms[i] == b) { ib = i; break; } |
---|
2854 | } |
---|
2855 | |
---|
2856 | for (int i = 1; i < int(subblossoms.size()); i += 2) { |
---|
2857 | int sb = subblossoms[(ib + i) % subblossoms.size()]; |
---|
2858 | int tb = subblossoms[(ib + i + 1) % subblossoms.size()]; |
---|
2859 | |
---|
2860 | Arc m = (*_blossom_data)[tb].next; |
---|
2861 | extractBlossom(sb, _graph.target(m), _graph.oppositeArc(m)); |
---|
2862 | extractBlossom(tb, _graph.source(m), m); |
---|
2863 | } |
---|
2864 | extractBlossom(subblossoms[ib], base, matching); |
---|
2865 | |
---|
2866 | int en = _blossom_node_list.size(); |
---|
2867 | |
---|
2868 | _blossom_potential.push_back(BlossomVariable(bn, en, pot)); |
---|
2869 | } |
---|
2870 | } |
---|
2871 | |
---|
2872 | void extractMatching() { |
---|
2873 | std::vector<int> blossoms; |
---|
2874 | for (typename BlossomSet::ClassIt c(*_blossom_set); c != INVALID; ++c) { |
---|
2875 | blossoms.push_back(c); |
---|
2876 | } |
---|
2877 | |
---|
2878 | for (int i = 0; i < int(blossoms.size()); ++i) { |
---|
2879 | |
---|
2880 | Value offset = (*_blossom_data)[blossoms[i]].offset; |
---|
2881 | (*_blossom_data)[blossoms[i]].pot += 2 * offset; |
---|
2882 | for (typename BlossomSet::ItemIt n(*_blossom_set, blossoms[i]); |
---|
2883 | n != INVALID; ++n) { |
---|
2884 | (*_node_data)[(*_node_index)[n]].pot -= offset; |
---|
2885 | } |
---|
2886 | |
---|
2887 | Arc matching = (*_blossom_data)[blossoms[i]].next; |
---|
2888 | Node base = _graph.source(matching); |
---|
2889 | extractBlossom(blossoms[i], base, matching); |
---|
2890 | } |
---|
2891 | } |
---|
2892 | |
---|
2893 | public: |
---|
2894 | |
---|
2895 | /// \brief Constructor |
---|
2896 | /// |
---|
2897 | /// Constructor. |
---|
2898 | MaxWeightedPerfectMatching(const Graph& graph, const WeightMap& weight) |
---|
2899 | : _graph(graph), _weight(weight), _matching(0), |
---|
2900 | _node_potential(0), _blossom_potential(), _blossom_node_list(), |
---|
2901 | _node_num(0), _blossom_num(0), |
---|
2902 | |
---|
2903 | _blossom_index(0), _blossom_set(0), _blossom_data(0), |
---|
2904 | _node_index(0), _node_heap_index(0), _node_data(0), |
---|
2905 | _tree_set_index(0), _tree_set(0), |
---|
2906 | |
---|
2907 | _delta2_index(0), _delta2(0), |
---|
2908 | _delta3_index(0), _delta3(0), |
---|
2909 | _delta4_index(0), _delta4(0), |
---|
2910 | |
---|
2911 | _delta_sum() {} |
---|
2912 | |
---|
2913 | ~MaxWeightedPerfectMatching() { |
---|
2914 | destroyStructures(); |
---|
2915 | } |
---|
2916 | |
---|
2917 | /// \name Execution Control |
---|
2918 | /// The simplest way to execute the algorithm is to use the |
---|
2919 | /// \ref run() member function. |
---|
2920 | |
---|
2921 | ///@{ |
---|
2922 | |
---|
2923 | /// \brief Initialize the algorithm |
---|
2924 | /// |
---|
2925 | /// This function initializes the algorithm. |
---|
2926 | void init() { |
---|
2927 | createStructures(); |
---|
2928 | |
---|
2929 | for (ArcIt e(_graph); e != INVALID; ++e) { |
---|
2930 | (*_node_heap_index)[e] = BinHeap<Value, IntArcMap>::PRE_HEAP; |
---|
2931 | } |
---|
2932 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
2933 | (*_delta3_index)[e] = _delta3->PRE_HEAP; |
---|
2934 | } |
---|
2935 | for (int i = 0; i < _blossom_num; ++i) { |
---|
2936 | (*_delta2_index)[i] = _delta2->PRE_HEAP; |
---|
2937 | (*_delta4_index)[i] = _delta4->PRE_HEAP; |
---|
2938 | } |
---|
2939 | |
---|
2940 | int index = 0; |
---|
2941 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
2942 | Value max = - std::numeric_limits<Value>::max(); |
---|
2943 | for (OutArcIt e(_graph, n); e != INVALID; ++e) { |
---|
2944 | if (_graph.target(e) == n) continue; |
---|
2945 | if ((dualScale * _weight[e]) / 2 > max) { |
---|
2946 | max = (dualScale * _weight[e]) / 2; |
---|
2947 | } |
---|
2948 | } |
---|
2949 | (*_node_index)[n] = index; |
---|
2950 | (*_node_data)[index].pot = max; |
---|
2951 | int blossom = |
---|
2952 | _blossom_set->insert(n, std::numeric_limits<Value>::max()); |
---|
2953 | |
---|
2954 | _tree_set->insert(blossom); |
---|
2955 | |
---|
2956 | (*_blossom_data)[blossom].status = EVEN; |
---|
2957 | (*_blossom_data)[blossom].pred = INVALID; |
---|
2958 | (*_blossom_data)[blossom].next = INVALID; |
---|
2959 | (*_blossom_data)[blossom].pot = 0; |
---|
2960 | (*_blossom_data)[blossom].offset = 0; |
---|
2961 | ++index; |
---|
2962 | } |
---|
2963 | for (EdgeIt e(_graph); e != INVALID; ++e) { |
---|
2964 | int si = (*_node_index)[_graph.u(e)]; |
---|
2965 | int ti = (*_node_index)[_graph.v(e)]; |
---|
2966 | if (_graph.u(e) != _graph.v(e)) { |
---|
2967 | _delta3->push(e, ((*_node_data)[si].pot + (*_node_data)[ti].pot - |
---|
2968 | dualScale * _weight[e]) / 2); |
---|
2969 | } |
---|
2970 | } |
---|
2971 | } |
---|
2972 | |
---|
2973 | /// \brief Start the algorithm |
---|
2974 | /// |
---|
2975 | /// This function starts the algorithm. |
---|
2976 | /// |
---|
2977 | /// \pre \ref init() must be called before using this function. |
---|
2978 | bool start() { |
---|
2979 | enum OpType { |
---|
2980 | D2, D3, D4 |
---|
2981 | }; |
---|
2982 | |
---|
2983 | int unmatched = _node_num; |
---|
2984 | while (unmatched > 0) { |
---|
2985 | Value d2 = !_delta2->empty() ? |
---|
2986 | _delta2->prio() : std::numeric_limits<Value>::max(); |
---|
2987 | |
---|
2988 | Value d3 = !_delta3->empty() ? |
---|
2989 | _delta3->prio() : std::numeric_limits<Value>::max(); |
---|
2990 | |
---|
2991 | Value d4 = !_delta4->empty() ? |
---|
2992 | _delta4->prio() : std::numeric_limits<Value>::max(); |
---|
2993 | |
---|
2994 | _delta_sum = d2; OpType ot = D2; |
---|
2995 | if (d3 < _delta_sum) { _delta_sum = d3; ot = D3; } |
---|
2996 | if (d4 < _delta_sum) { _delta_sum = d4; ot = D4; } |
---|
2997 | |
---|
2998 | if (_delta_sum == std::numeric_limits<Value>::max()) { |
---|
2999 | return false; |
---|
3000 | } |
---|
3001 | |
---|
3002 | switch (ot) { |
---|
3003 | case D2: |
---|
3004 | { |
---|
3005 | int blossom = _delta2->top(); |
---|
3006 | Node n = _blossom_set->classTop(blossom); |
---|
3007 | Arc e = (*_node_data)[(*_node_index)[n]].heap.top(); |
---|
3008 | extendOnArc(e); |
---|
3009 | } |
---|
3010 | break; |
---|
3011 | case D3: |
---|
3012 | { |
---|
3013 | Edge e = _delta3->top(); |
---|
3014 | |
---|
3015 | int left_blossom = _blossom_set->find(_graph.u(e)); |
---|
3016 | int right_blossom = _blossom_set->find(_graph.v(e)); |
---|
3017 | |
---|
3018 | if (left_blossom == right_blossom) { |
---|
3019 | _delta3->pop(); |
---|
3020 | } else { |
---|
3021 | int left_tree = _tree_set->find(left_blossom); |
---|
3022 | int right_tree = _tree_set->find(right_blossom); |
---|
3023 | |
---|
3024 | if (left_tree == right_tree) { |
---|
3025 | shrinkOnEdge(e, left_tree); |
---|
3026 | } else { |
---|
3027 | augmentOnEdge(e); |
---|
3028 | unmatched -= 2; |
---|
3029 | } |
---|
3030 | } |
---|
3031 | } break; |
---|
3032 | case D4: |
---|
3033 | splitBlossom(_delta4->top()); |
---|
3034 | break; |
---|
3035 | } |
---|
3036 | } |
---|
3037 | extractMatching(); |
---|
3038 | return true; |
---|
3039 | } |
---|
3040 | |
---|
3041 | /// \brief Run the algorithm. |
---|
3042 | /// |
---|
3043 | /// This method runs the \c %MaxWeightedPerfectMatching algorithm. |
---|
3044 | /// |
---|
3045 | /// \note mwpm.run() is just a shortcut of the following code. |
---|
3046 | /// \code |
---|
3047 | /// mwpm.init(); |
---|
3048 | /// mwpm.start(); |
---|
3049 | /// \endcode |
---|
3050 | bool run() { |
---|
3051 | init(); |
---|
3052 | return start(); |
---|
3053 | } |
---|
3054 | |
---|
3055 | /// @} |
---|
3056 | |
---|
3057 | /// \name Primal Solution |
---|
3058 | /// Functions to get the primal solution, i.e. the maximum weighted |
---|
3059 | /// perfect matching.\n |
---|
3060 | /// Either \ref run() or \ref start() function should be called before |
---|
3061 | /// using them. |
---|
3062 | |
---|
3063 | /// @{ |
---|
3064 | |
---|
3065 | /// \brief Return the weight of the matching. |
---|
3066 | /// |
---|
3067 | /// This function returns the weight of the found matching. |
---|
3068 | /// |
---|
3069 | /// \pre Either run() or start() must be called before using this function. |
---|
3070 | Value matchingWeight() const { |
---|
3071 | Value sum = 0; |
---|
3072 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
3073 | if ((*_matching)[n] != INVALID) { |
---|
3074 | sum += _weight[(*_matching)[n]]; |
---|
3075 | } |
---|
3076 | } |
---|
3077 | return sum /= 2; |
---|
3078 | } |
---|
3079 | |
---|
3080 | /// \brief Return \c true if the given edge is in the matching. |
---|
3081 | /// |
---|
3082 | /// This function returns \c true if the given edge is in the found |
---|
3083 | /// matching. |
---|
3084 | /// |
---|
3085 | /// \pre Either run() or start() must be called before using this function. |
---|
3086 | bool matching(const Edge& edge) const { |
---|
3087 | return static_cast<const Edge&>((*_matching)[_graph.u(edge)]) == edge; |
---|
3088 | } |
---|
3089 | |
---|
3090 | /// \brief Return the matching arc (or edge) incident to the given node. |
---|
3091 | /// |
---|
3092 | /// This function returns the matching arc (or edge) incident to the |
---|
3093 | /// given node in the found matching or \c INVALID if the node is |
---|
3094 | /// not covered by the matching. |
---|
3095 | /// |
---|
3096 | /// \pre Either run() or start() must be called before using this function. |
---|
3097 | Arc matching(const Node& node) const { |
---|
3098 | return (*_matching)[node]; |
---|
3099 | } |
---|
3100 | |
---|
3101 | /// \brief Return a const reference to the matching map. |
---|
3102 | /// |
---|
3103 | /// This function returns a const reference to a node map that stores |
---|
3104 | /// the matching arc (or edge) incident to each node. |
---|
3105 | const MatchingMap& matchingMap() const { |
---|
3106 | return *_matching; |
---|
3107 | } |
---|
3108 | |
---|
3109 | /// \brief Return the mate of the given node. |
---|
3110 | /// |
---|
3111 | /// This function returns the mate of the given node in the found |
---|
3112 | /// matching or \c INVALID if the node is not covered by the matching. |
---|
3113 | /// |
---|
3114 | /// \pre Either run() or start() must be called before using this function. |
---|
3115 | Node mate(const Node& node) const { |
---|
3116 | return _graph.target((*_matching)[node]); |
---|
3117 | } |
---|
3118 | |
---|
3119 | /// @} |
---|
3120 | |
---|
3121 | /// \name Dual Solution |
---|
3122 | /// Functions to get the dual solution.\n |
---|
3123 | /// Either \ref run() or \ref start() function should be called before |
---|
3124 | /// using them. |
---|
3125 | |
---|
3126 | /// @{ |
---|
3127 | |
---|
3128 | /// \brief Return the value of the dual solution. |
---|
3129 | /// |
---|
3130 | /// This function returns the value of the dual solution. |
---|
3131 | /// It should be equal to the primal value scaled by \ref dualScale |
---|
3132 | /// "dual scale". |
---|
3133 | /// |
---|
3134 | /// \pre Either run() or start() must be called before using this function. |
---|
3135 | Value dualValue() const { |
---|
3136 | Value sum = 0; |
---|
3137 | for (NodeIt n(_graph); n != INVALID; ++n) { |
---|
3138 | sum += nodeValue(n); |
---|
3139 | } |
---|
3140 | for (int i = 0; i < blossomNum(); ++i) { |
---|
3141 | sum += blossomValue(i) * (blossomSize(i) / 2); |
---|
3142 | } |
---|
3143 | return sum; |
---|
3144 | } |
---|
3145 | |
---|
3146 | /// \brief Return the dual value (potential) of the given node. |
---|
3147 | /// |
---|
3148 | /// This function returns the dual value (potential) of the given node. |
---|
3149 | /// |
---|
3150 | /// \pre Either run() or start() must be called before using this function. |
---|
3151 | Value nodeValue(const Node& n) const { |
---|
3152 | return (*_node_potential)[n]; |
---|
3153 | } |
---|
3154 | |
---|
3155 | /// \brief Return the number of the blossoms in the basis. |
---|
3156 | /// |
---|
3157 | /// This function returns the number of the blossoms in the basis. |
---|
3158 | /// |
---|
3159 | /// \pre Either run() or start() must be called before using this function. |
---|
3160 | /// \see BlossomIt |
---|
3161 | int blossomNum() const { |
---|
3162 | return _blossom_potential.size(); |
---|
3163 | } |
---|
3164 | |
---|
3165 | /// \brief Return the number of the nodes in the given blossom. |
---|
3166 | /// |
---|
3167 | /// This function returns the number of the nodes in the given blossom. |
---|
3168 | /// |
---|
3169 | /// \pre Either run() or start() must be called before using this function. |
---|
3170 | /// \see BlossomIt |
---|
3171 | int blossomSize(int k) const { |
---|
3172 | return _blossom_potential[k].end - _blossom_potential[k].begin; |
---|
3173 | } |
---|
3174 | |
---|
3175 | /// \brief Return the dual value (ptential) of the given blossom. |
---|
3176 | /// |
---|
3177 | /// This function returns the dual value (ptential) of the given blossom. |
---|
3178 | /// |
---|
3179 | /// \pre Either run() or start() must be called before using this function. |
---|
3180 | Value blossomValue(int k) const { |
---|
3181 | return _blossom_potential[k].value; |
---|
3182 | } |
---|
3183 | |
---|
3184 | /// \brief Iterator for obtaining the nodes of a blossom. |
---|
3185 | /// |
---|
3186 | /// This class provides an iterator for obtaining the nodes of the |
---|
3187 | /// given blossom. It lists a subset of the nodes. |
---|
3188 | /// Before using this iterator, you must allocate a |
---|
3189 | /// MaxWeightedPerfectMatching class and execute it. |
---|
3190 | class BlossomIt { |
---|
3191 | public: |
---|
3192 | |
---|
3193 | /// \brief Constructor. |
---|
3194 | /// |
---|
3195 | /// Constructor to get the nodes of the given variable. |
---|
3196 | /// |
---|
3197 | /// \pre Either \ref MaxWeightedPerfectMatching::run() "algorithm.run()" |
---|
3198 | /// or \ref MaxWeightedPerfectMatching::start() "algorithm.start()" |
---|
3199 | /// must be called before initializing this iterator. |
---|
3200 | BlossomIt(const MaxWeightedPerfectMatching& algorithm, int variable) |
---|
3201 | : _algorithm(&algorithm) |
---|
3202 | { |
---|
3203 | _index = _algorithm->_blossom_potential[variable].begin; |
---|
3204 | _last = _algorithm->_blossom_potential[variable].end; |
---|
3205 | } |
---|
3206 | |
---|
3207 | /// \brief Conversion to \c Node. |
---|
3208 | /// |
---|
3209 | /// Conversion to \c Node. |
---|
3210 | operator Node() const { |
---|
3211 | return _algorithm->_blossom_node_list[_index]; |
---|
3212 | } |
---|
3213 | |
---|
3214 | /// \brief Increment operator. |
---|
3215 | /// |
---|
3216 | /// Increment operator. |
---|
3217 | BlossomIt& operator++() { |
---|
3218 | ++_index; |
---|
3219 | return *this; |
---|
3220 | } |
---|
3221 | |
---|
3222 | /// \brief Validity checking |
---|
3223 | /// |
---|
3224 | /// This function checks whether the iterator is invalid. |
---|
3225 | bool operator==(Invalid) const { return _index == _last; } |
---|
3226 | |
---|
3227 | /// \brief Validity checking |
---|
3228 | /// |
---|
3229 | /// This function checks whether the iterator is valid. |
---|
3230 | bool operator!=(Invalid) const { return _index != _last; } |
---|
3231 | |
---|
3232 | private: |
---|
3233 | const MaxWeightedPerfectMatching* _algorithm; |
---|
3234 | int _last; |
---|
3235 | int _index; |
---|
3236 | }; |
---|
3237 | |
---|
3238 | /// @} |
---|
3239 | |
---|
3240 | }; |
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3241 | |
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3242 | } //END OF NAMESPACE LEMON |
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3243 | |
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3244 | #endif //LEMON_MAX_MATCHING_H |
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